College Algebra Exam 1 Review – Step-by-Step Guidance

{"type":"doc","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"{\"type\":\"doc\",\"content\":[{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":3},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Q1a. Simplify: (5 - 3i) - (11 + 4i)\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Background\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Topic: Complex Numbers\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"This question tests your ability to add and subtract complex numbers, combining real and imaginary parts.\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Key Terms and Formulas:\"}]},{\"type\":\"bulletList\",\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Complex number: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"a + bi\"}},{\"type\":\"text\",\"text\":\" where \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"a\"}},{\"type\":\"text\",\"text\":\" is the real part and \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"b\"}},{\"type\":\"text\",\"text\":\" is the imaginary part.\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"To add/subtract: Combine real parts and imaginary parts separately.\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Step-by-Step Guidance\"}]},{\"type\":\"orderedList\",\"attrs\":{\"start\":1,\"type\":null},\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Write both complex numbers: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"5 - 3i\"}},{\"type\":\"text\",\"text\":\" and \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"11 + 4i\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Subtract the real parts: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"5 - 11\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Subtract the imaginary parts: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"-3i - 4i\"}},{\"type\":\"text\",\"text\":\".\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Try solving on your own before revealing the answer!\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":3},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Q1b. Simplify: -3i(6 - i)\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Background\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Topic: Complex Numbers – Multiplication\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"This question tests your ability to multiply a complex number by an imaginary number.\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Key Terms and Formulas:\"}]},{\"type\":\"bulletList\",\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Imaginary unit: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"i\"}},{\"type\":\"text\",\"text\":\", where \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"i^2 = -1\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Distributive property: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"a(b + c) = ab + ac\"}},{\"type\":\"text\",\"text\":\".\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Step-by-Step Guidance\"}]},{\"type\":\"orderedList\",\"attrs\":{\"start\":1,\"type\":null},\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Apply the distributive property: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"-3i \\\\times 6\"}},{\"type\":\"text\",\"text\":\" and \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"-3i \\\\times (-i)\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Calculate \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"-3i \\\\times 6\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Calculate \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"-3i \\\\times (-i)\"}},{\"type\":\"text\",\"text\":\", remembering \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"i \\\\times i = i^2 = -1\"}},{\"type\":\"text\",\"text\":\".\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Try solving on your own before revealing the answer!\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":3},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Q1c. Simplify: (3 - 4i)(-2 + 4i)\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Background\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Topic: Complex Numbers – Multiplication\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"This question tests your ability to multiply two complex numbers using the distributive property (FOIL method).\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Key Terms and Formulas:\"}]},{\"type\":\"bulletList\",\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"FOIL: First, Outside, Inside, Last for binomial multiplication.\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"i^2 = -1\"}},{\"type\":\"text\",\"text\":\".\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Step-by-Step Guidance\"}]},{\"type\":\"orderedList\",\"attrs\":{\"start\":1,\"type\":null},\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Multiply \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"(3 - 4i)\"}},{\"type\":\"text\",\"text\":\" by \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"(-2 + 4i)\"}},{\"type\":\"text\",\"text\":\" using FOIL:\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"First: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"3 \\\\times -2\"}}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Outside: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"3 \\\\times 4i\"}}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Inside: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"-4i \\\\times -2\"}}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Last: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"-4i \\\\times 4i\"}}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Try solving on your own before revealing the answer!\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":3},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Q1d. Simplify: (\\\\frac{3}{4} - \\\\frac{1}{2}i)(\\\\frac{3}{4} + \\\\frac{1}{2}i)\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Background\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Topic: Complex Numbers – Multiplication (Conjugates)\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"This question tests your ability to multiply conjugate complex numbers, which results in a real number.\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Key Terms and Formulas:\"}]},{\"type\":\"bulletList\",\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Conjugate: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"a + bi\"}},{\"type\":\"text\",\"text\":\" and \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"a - bi\"}}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"(a + bi)(a - bi) = a^2 - b^2i^2\"}}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"i^2 = -1\"}}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Step-by-Step Guidance\"}]},{\"type\":\"orderedList\",\"attrs\":{\"start\":1,\"type\":null},\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Identify \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"a = \\\\frac{3}{4}\"}},{\"type\":\"text\",\"text\":\" and \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"b = \\\\frac{1}{2}\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Apply the formula: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"(a + bi)(a - bi) = a^2 - b^2i^2\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Calculate \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"a^2\"}},{\"type\":\"text\",\"text\":\" and \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"b^2\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Substitute \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"i^2 = -1\"}},{\"type\":\"text\",\"text\":\" and simplify.\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Try solving on your own before revealing the answer!\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":3},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Q1e. Simplify: \\\\frac{6}{5 + i}\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Background\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Topic: Complex Numbers – Rationalizing Denominators\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"This question tests your ability to rationalize the denominator of a complex fraction.\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Key Terms and Formulas:\"}]},{\"type\":\"bulletList\",\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"To rationalize: Multiply numerator and denominator by the conjugate of the denominator.\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Conjugate of \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"5 + i\"}},{\"type\":\"text\",\"text\":\" is \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"5 - i\"}},{\"type\":\"text\",\"text\":\".\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Step-by-Step Guidance\"}]},{\"type\":\"orderedList\",\"attrs\":{\"start\":1,\"type\":null},\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Multiply numerator and denominator by \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"5 - i\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Write: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\frac{6}{5 + i} \\\\times \\\\frac{5 - i}{5 - i}\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Expand numerator: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"6 \\\\times (5 - i)\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Expand denominator: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"(5 + i)(5 - i)\"}},{\"type\":\"text\",\"text\":\".\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Try solving on your own before revealing the answer!\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":3},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Q1f. Simplify: \\\\frac{2 - i}{5 + 2i}\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Background\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Topic: Complex Numbers – Rationalizing Denominators\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"This question tests your ability to rationalize the denominator of a complex fraction.\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Key Terms and Formulas:\"}]},{\"type\":\"bulletList\",\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Conjugate of \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"5 + 2i\"}},{\"type\":\"text\",\"text\":\" is \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"5 - 2i\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Multiply numerator and denominator by the conjugate.\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Step-by-Step Guidance\"}]},{\"type\":\"orderedList\",\"attrs\":{\"start\":1,\"type\":null},\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Multiply numerator and denominator by \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"5 - 2i\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Write: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\frac{2 - i}{5 + 2i} \\\\times \\\\frac{5 - 2i}{5 - 2i}\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Expand numerator: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"(2 - i)(5 - 2i)\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Expand denominator: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"(5 + 2i)(5 - 2i)\"}},{\"type\":\"text\",\"text\":\".\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Try solving on your own before revealing the answer!\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":3},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Q2. Solve the quadratic equation: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"x^2 - 5x - 14 = 0\"}}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Background\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Topic: Quadratic Equations\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"This question tests your ability to solve quadratic equations by factoring, using the quadratic formula, or the square root property.\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Key Terms and Formulas:\"}]},{\"type\":\"bulletList\",\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Quadratic formula: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"x = \\\\frac{-b \\\\pm \\\\sqrt{b^2 - 4ac}}{2a}\"}}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Standard form: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"ax^2 + bx + c = 0\"}}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Step-by-Step Guidance\"}]},{\"type\":\"orderedList\",\"attrs\":{\"start\":1,\"type\":null},\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Identify \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"a = 1\"}},{\"type\":\"text\",\"text\":\", \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"b = -5\"}},{\"type\":\"text\",\"text\":\", \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"c = -14\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Write the quadratic formula: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"x = \\\\frac{-b \\\\pm \\\\sqrt{b^2 - 4ac}}{2a}\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Plug in the values for \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"a\"}},{\"type\":\"text\",\"text\":\", \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"b\"}},{\"type\":\"text\",\"text\":\", and \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"c\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Calculate the discriminant: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"b^2 - 4ac\"}},{\"type\":\"text\",\"text\":\".\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Try solving on your own before revealing the answer!\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":3},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Q3. Solve the quadratic equation: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"6x^2 - x = 5\"}}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Background\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Topic: Quadratic Equations\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"This question tests your ability to solve quadratic equations by rearranging to standard form and using factoring or the quadratic formula.\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Key Terms and Formulas:\"}]},{\"type\":\"bulletList\",\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Quadratic formula: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"x = \\\\frac{-b \\\\pm \\\\sqrt{b^2 - 4ac}}{2a}\"}}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Standard form: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"ax^2 + bx + c = 0\"}}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Step-by-Step Guidance\"}]},{\"type\":\"orderedList\",\"attrs\":{\"start\":1,\"type\":null},\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Move all terms to one side: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"6x^2 - x - 5 = 0\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Identify \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"a = 6\"}},{\"type\":\"text\",\"text\":\", \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"b = -1\"}},{\"type\":\"text\",\"text\":\", \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"c = -5\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Write the quadratic formula.\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Plug in the values for \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"a\"}},{\"type\":\"text\",\"text\":\", \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"b\"}},{\"type\":\"text\",\"text\":\", and \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"c\"}},{\"type\":\"text\",\"text\":\".\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Try solving on your own before revealing the answer!\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":3},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Q4. Solve the quadratic equation: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"12x^2 = 25x\"}}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Background\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Topic: Quadratic Equations\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"This question tests your ability to solve quadratic equations by rearranging to standard form and using factoring or the quadratic formula.\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Key Terms and Formulas:\"}]},{\"type\":\"bulletList\",\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Quadratic formula: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"x = \\\\frac{-b \\\\pm \\\\sqrt{b^2 - 4ac}}{2a}\"}}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Standard form: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"ax^2 + bx + c = 0\"}}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Step-by-Step Guidance\"}]},{\"type\":\"orderedList\",\"attrs\":{\"start\":1,\"type\":null},\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Move all terms to one side: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"12x^2 - 25x = 0\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Factor out \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"x\"}},{\"type\":\"text\",\"text\":\": \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"x(12x - 25) = 0\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Set each factor equal to zero: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"x = 0\"}},{\"type\":\"text\",\"text\":\" or \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"12x - 25 = 0\"}},{\"type\":\"text\",\"text\":\".\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Try solving on your own before revealing the answer!\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":3},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Q5. Solve the quadratic equation: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"9x^2 - 16 = 0\"}}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Background\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Topic: Quadratic Equations – Difference of Squares\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"This question tests your ability to solve quadratic equations using factoring, specifically the difference of squares.\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Key Terms and Formulas:\"}]},{\"type\":\"bulletList\",\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Difference of squares: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"a^2 - b^2 = (a - b)(a + b)\"}}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Step-by-Step Guidance\"}]},{\"type\":\"orderedList\",\"attrs\":{\"start\":1,\"type\":null},\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Recognize \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"9x^2 - 16\"}},{\"type\":\"text\",\"text\":\" as a difference of squares.\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Write: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"9x^2 - 16 = (3x)^2 - (4)^2\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Factor: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"(3x - 4)(3x + 4) = 0\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Set each factor equal to zero.\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Try solving on your own before revealing the answer!\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":3},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Q6. Solve the quadratic equation: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"(x - 2)^2 - 36 = 0\"}}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Background\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Topic: Quadratic Equations – Square Root Property\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"This question tests your ability to solve quadratic equations using the square root property.\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Key Terms and Formulas:\"}]},{\"type\":\"bulletList\",\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Square root property: If \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"x^2 = a\"}},{\"type\":\"text\",\"text\":\", then \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"x = \\\\pm \\\\sqrt{a}\"}},{\"type\":\"text\",\"text\":\".\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Step-by-Step Guidance\"}]},{\"type\":\"orderedList\",\"attrs\":{\"start\":1,\"type\":null},\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Add "},{"type":"inlineMath","attrs":{"latex":"36\"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\" to both sides: \"}},{\"type\":\"text\",\"text\":\"(x - 2)^2 = 36"}},{"type":"text","text":".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Take the square root of both sides: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"x - 2 = \\\\pm \\\\sqrt{36}\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Solve for \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"x\"}},{\"type\":\"text\",\"text\":\" by adding $2"},{"type":"inlineMath","attrs":{"latex":" to both sides.\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Try solving on your own before revealing the answer!\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":3},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Q7. Solve the equation: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"x^3 + x^2 = 4x + 4\"}}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Background\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Topic: Polynomial Equations\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"This question tests your ability to solve cubic equations by rearranging and factoring.\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Key Terms and Formulas:\"}]},{\"type\":\"bulletList\",\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Standard form: Move all terms to one side.\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Factoring: Look for common factors or use grouping.\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Step-by-Step Guidance\"}]},{\"type\":\"orderedList\",\"attrs\":{\"start\":1,\"type\":null},\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Move all terms to one side: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"x^3 + x^2 - 4x - 4 = 0\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Try factoring by grouping: Group terms as \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"(x^3 + x^2)\"}},{\"type\":\"text\",\"text\":\" and \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"(-4x - 4)\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Factor each group: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"x^2(x + 1)\"}},{\"type\":\"text\",\"text\":\" and \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"-4(x + 1)\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Factor out \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"(x + 1)\"}},{\"type\":\"text\",\"text\":\": \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"(x + 1)(x^2 - 4)\"}},{\"type\":\"text\",\"text\":\".\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Try solving on your own before revealing the answer!\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":3},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Q8. Solve the equation: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"(x - 4)^{3/2} = 27\"}}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Background\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Topic: Radical Equations\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"This question tests your ability to solve equations involving rational exponents.\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Key Terms and Formulas:\"}]},{\"type\":\"bulletList\",\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Rational exponent: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"a^{m/n} = (\\\\sqrt[n]{a})^m\"}}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Step-by-Step Guidance\"}]},{\"type\":\"orderedList\",\"attrs\":{\"start\":1,\"type\":null},\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Rewrite $27\"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\" as $3^3\"}},{\"type\":\"text\",\"text\":\" to make calculations easier.\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"To solve for \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"x\"}},{\"type\":\"text\",\"text\":\", raise both sides to the reciprocal exponent \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"2/3\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Apply: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"[(x - 4)^{3/2}]^{2/3} = 27^{2/3}\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Simplify the left side to \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"x - 4\"}},{\"type\":\"text\",\"text\":\".\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Try solving on your own before revealing the answer!\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":3},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Q9. Solve the equation: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"8x^{5/3} - 24 = 0\"}}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Background\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Topic: Radical Equations\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"This question tests your ability to solve equations with rational exponents.\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Key Terms and Formulas:\"}]},{\"type\":\"bulletList\",\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Rational exponent: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"x^{m/n} = (\\\\sqrt[n]{x})^m\"}}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Step-by-Step Guidance\"}]},{\"type\":\"orderedList\",\"attrs\":{\"start\":1,\"type\":null},\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Add $24\"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\" to both sides: $8x^{5/3} = 24\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Divide both sides by $8\"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\": \"}},{\"type\":\"text\",\"text\":\"x^{5/3} = 3"}},{"type":"text","text":".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Raise both sides to the reciprocal exponent \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"3/5\"}},{\"type\":\"text\",\"text\":\".\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Try solving on your own before revealing the answer!\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":3},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Q10. Solve: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"x + 2 + \\\\frac{3x + 7}{1}\"}}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Background\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Topic: Linear Equations\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"This question tests your ability to solve linear equations, including combining like terms.\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Key Terms and Formulas:\"}]},{\"type\":\"bulletList\",\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Combine like terms: Add or subtract terms with the same variable.\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Step-by-Step Guidance\"}]},{\"type\":\"orderedList\",\"attrs\":{\"start\":1,\"type\":null},\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Recognize that \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\frac{3x + 7}{1} = 3x + 7\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Combine all terms: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"x + 2 + 3x + 7\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Combine like terms: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"x + 3x\"}},{\"type\":\"text\",\"text\":\" and \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"2 + 7\"}},{\"type\":\"text\",\"text\":\".\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Try solving on your own before revealing the answer!\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":3},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Q11. Solve: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"2x + 15 - 6 = x\"}}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Background\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Topic: Linear Equations\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"This question tests your ability to solve linear equations by isolating the variable.\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Key Terms and Formulas:\"}]},{\"type\":\"bulletList\",\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Combine like terms and isolate \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"x\"}},{\"type\":\"text\",\"text\":\".\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Step-by-Step Guidance\"}]},{\"type\":\"orderedList\",\"attrs\":{\"start\":1,\"type\":null},\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Combine \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"15 - 6\"}},{\"type\":\"text\",\"text\":\" to get $9"},{"type":"inlineMath","attrs":{"latex":".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Write: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"2x + 9 = x\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Subtract \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"x\"}},{\"type\":\"text\",\"text\":\" from both sides.\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Try solving on your own before revealing the answer!\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":3},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Q12. Solve: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"4|1 - \\\\frac{3}{4}x| + 7 = 10\"}}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Background\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Topic: Absolute Value Equations\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"This question tests your ability to solve equations involving absolute value.\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Key Terms and Formulas:\"}]},{\"type\":\"bulletList\",\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Absolute value: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"|a|\"}},{\"type\":\"text\",\"text\":\" is the distance from zero, always non-negative.\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Step-by-Step Guidance\"}]},{\"type\":\"orderedList\",\"attrs\":{\"start\":1,\"type\":null},\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Subtract $7\"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\" from both sides: $4|1 - \\\\frac{3}{4}x| = 3\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Divide both sides by $4\"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\": \"}},{\"type\":\"text\",\"text\":\"|1 - \\\\frac{3}{4}x| = \\\\frac{3}{4}"}},{"type":"text","text":".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Set up two equations: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"1 - \\\\frac{3}{4}x = \\\\frac{3}{4}\"}},{\"type\":\"text\",\"text\":\" and \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"1 - \\\\frac{3}{4}x = -\\\\frac{3}{4}\"}},{\"type\":\"text\",\"text\":\".\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Try solving on your own before revealing the answer!\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":3},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Q13. Solve: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"2|x - 3| - 6 = 10\"}}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Background\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Topic: Absolute Value Equations\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"This question tests your ability to solve equations involving absolute value.\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Key Terms and Formulas:\"}]},{\"type\":\"bulletList\",\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Absolute value: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"|a|\"}},{\"type\":\"text\",\"text\":\" is always non-negative.\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Step-by-Step Guidance\"}]},{\"type\":\"orderedList\",\"attrs\":{\"start\":1,\"type\":null},\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Add "},{"type":"inlineMath","attrs":{"latex":"6\"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\" to both sides: $2|x - 3| = 16\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Divide both sides by $2\"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\": \"}},{\"type\":\"text\",\"text\":\"|x - 3| = 8"}},{"type":"text","text":".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Set up two equations: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"x - 3 = 8\"}},{\"type\":\"text\",\"text\":\" and \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"x - 3 = -8\"}},{\"type\":\"text\",\"text\":\".\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Try solving on your own before revealing the answer!\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":3},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Q14. Car rental agency problem\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Background\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Topic: Linear Equations – Word Problems\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"This question tests your ability to set up and solve equations based on a real-world scenario involving cost comparison.\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Key Terms and Formulas:\"}]},{\"type\":\"bulletList\",\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Let \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"m\"}},{\"type\":\"text\",\"text\":\" be the number of miles driven.\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Unlimited plan: $40"},{"type":"inlineMath","attrs":{"latex":" per day.\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Other plan: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"24 + 0.20m\"}},{\"type\":\"text\",\"text\":\" per day.\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Step-by-Step Guidance\"}]},{\"type\":\"orderedList\",\"attrs\":{\"start\":1,\"type\":null},\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Set up the inequality: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"24 + 0.20m \\\\leq 40\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Subtract $24\"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\" from both sides: $0.20m \\\\leq 16\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Solve for \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"m\"}},{\"type\":\"text\",\"text\":\" by dividing both sides by \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"0.20\"}},{\"type\":\"text\",\"text\":\".\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Try solving on your own before revealing the answer!\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":3},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Q15. Toll road pass problem\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Background\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Topic: Linear Equations – Word Problems\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"This question tests your ability to set up and solve equations to compare costs and determine break-even points.\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Key Terms and Formulas:\"}]},{\"type\":\"bulletList\",\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Let \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"n\"}},{\"type\":\"text\",\"text\":\" be the number of times the road is used.\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Normal cost: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"5n\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Pass cost: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"30 + (5 \\\\times 0.7)n = 30 + 3.5n\"}},{\"type\":\"text\",\"text\":\".\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Step-by-Step Guidance\"}]},{\"type\":\"orderedList\",\"attrs\":{\"start\":1,\"type\":null},\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Set up the inequality: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"30 + 3.5n < 5n\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Subtract \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"3.5n\"}},{\"type\":\"text\",\"text\":\" from both sides: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"30 < 1.5n\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Solve for \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"n\"}},{\"type\":\"text\",\"text\":\" by dividing both sides by \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"1.5\"}},{\"type\":\"text\",\"text\":\".\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Try solving on your own before revealing the answer!\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":3},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Q16. Solve: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"-11 < 2x - 1 < -5\"}}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Background\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Topic: Compound Inequalities\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"This question tests your ability to solve compound inequalities.\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Key Terms and Formulas:\"}]},{\"type\":\"bulletList\",\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Compound inequality: Solve for \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"x\"}},{\"type\":\"text\",\"text\":\" in both parts.\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Step-by-Step Guidance\"}]},{\"type\":\"orderedList\",\"attrs\":{\"start\":1,\"type\":null},\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Add $1\"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\" to all parts: \"}},{\"type\":\"text\",\"text\":\"-10 < 2x < -4"}},{"type":"text","text":".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Divide all parts by "},{"type":"inlineMath","attrs":{"latex":"2\"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\": \"}},{\"type\":\"text\",\"text\":\"-5 < x < -2"}},{"type":"text","text":".\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Try solving on your own before revealing the answer!\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":3},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Q17. Solve: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"|3 - \\\\frac{3}{4}x| > 9\"}}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Background\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Topic: Absolute Value Inequalities\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"This question tests your ability to solve inequalities involving absolute value.\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Key Terms and Formulas:\"}]},{\"type\":\"bulletList\",\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"For \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"|A| > B\"}},{\"type\":\"text\",\"text\":\", \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"A > B\"}},{\"type\":\"text\",\"text\":\" or \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"A < -B\"}},{\"type\":\"text\",\"text\":\".\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Step-by-Step Guidance\"}]},{\"type\":\"orderedList\",\"attrs\":{\"start\":1,\"type\":null},\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Set up two inequalities: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"3 - \\\\frac{3}{4}x > 9\"}},{\"type\":\"text\",\"text\":\" and \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"3 - \\\\frac{3}{4}x < -9\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Solve each inequality for \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"x\"}},{\"type\":\"text\",\"text\":\".\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Try solving on your own before revealing the answer!\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":3},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Q18. Is the equation \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"2x + y^2 = 6\"}},{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\" a function? Why or why not?\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Background\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Topic: Functions – Definition\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"This question tests your understanding of what makes a relation a function.\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Key Terms and Formulas:\"}]},{\"type\":\"bulletList\",\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"A function assigns exactly one \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"y\"}},{\"type\":\"text\",\"text\":\" value for each \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"x\"}},{\"type\":\"text\",\"text\":\" value.\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Vertical line test: If a vertical line crosses the graph more than once, it's not a function.\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Step-by-Step Guidance\"}]},{\"type\":\"orderedList\",\"attrs\":{\"start\":1,\"type\":null},\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Try to solve for \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"y\"}},{\"type\":\"text\",\"text\":\" in terms of \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"x\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Notice that \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"y^2\"}},{\"type\":\"text\",\"text\":\" means for some \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"x\"}},{\"type\":\"text\",\"text\":\", there may be two \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"y\"}},{\"type\":\"text\",\"text\":\" values.\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Try answering on your own be