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College Algebra Unit 1 Exam Review

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Termini in questo insieme (27)

  • What do you add to both sides of the equation to solve by completing the square for x² + 14x = 6?
    Add \(49\) to both sides.
  • What are the values of a, b, and c in the quadratic formula for the equation x² = 4x + 4?
    a = 1, b = -4, c = -4.
  • Simplify the quadratic formula expression: x = \(\frac{-4 \pm \sqrt{4^2 - 4 \cdot 2 \cdot 3}\)}{2 \(\cdot\) 2}.
    x = \(\frac{-4 \pm \sqrt{16 - 24}\)}{4} = \(\frac{-4 \pm \sqrt{-8}\)}{4} = \(\frac{-4 \pm 2i\sqrt{2}\)}{4} = -1 \(\pm\) \(\frac{i\sqrt{2}\)}{2}.
  • Which method is most efficient for solving (x + 5)² = 36?
    Use the square root property.
  • Which method is most efficient for solving x² + 5x - 10 = 0?
    Use factoring and the zero-product principle.
  • Which method is most efficient for solving x² + 8x + 15 = 0?
    Use factoring and the zero-product principle.
  • Solve by factoring: x² - 3x - 28 = 0.
    The solution set is x = 7, -4.
  • Solve by factoring: 7x² + 14x = 0.
    The solution set is x = 0, -2.
  • Solve using the quadratic formula with a=1, b=13, c=8.
    The solution set is x = \(\frac{-13 \pm \sqrt{169 - 32}\)}{2} = \(\frac{-13 \pm \sqrt{137}\)}{2}.
  • Solve by completing the square: x² - 4x = 3.
    Add 4 to both sides: (x - 2)² = 7, so x = 2 \(\pm\) \(\sqrt{7}\).
  • Given solutions {2, -5} for ax² + bx + c = 0, what are a, b, and c?
    a = 1, b = 3, c = -10.
  • Solve by factoring: 3x⁴ - 108x² = 0.
    The solution set is x = 0, 6, -6.
  • Solve by factoring: x³ + 2x² = 81x + 162.
    The solution set is x = 9, -9, -2.
  • Solve the radical equation: \(\sqrt{2x + 5}\) = x - 5.
    The solution set is x = 10.
  • Solve the equation with rational exponents: x^{5/2} = 32.
    The solution set is x = 4.
  • Solve by substitution: x^{-2} + 2x^{-1} - 8 = 0.
    The solution set is x = -1, -\(\frac{1}{2}\).
  • Solve the absolute value equation: |2x - 1| = 7.
    The solution set is x = 4, -3.
  • In interval notation, what does [-7, 5) represent?
    All real numbers between -7 and 5, including -7 but not 5.
  • In interval notation, what does (2, ∞) represent?
    All real numbers greater than 2.
  • In interval notation, what does (-∞, 1] represent?
    All real numbers less than or equal to 1.
  • Express the solution set for the inequality 2x + 4 > 10 in interval notation.
    The solution set is (3, ∞).
  • Express the solution set for the inequality -5x ≤ 25 in interval notation.
    The solution set is [-5, ∞).
  • Express the solution set for the compound inequality -4 < 2x + 2 ≤ 2 in interval notation.
    The solution set is (-3, 0].
  • Solve the absolute value inequality |x + 5| ≤ 7 in interval notation.
    The solution set is [-12, 2].
  • Solve the absolute value inequality |x - 6| ≥ 2 in interval notation.
    The solution set is (-∞, 4] ∪ [8, ∞).
  • Rewrite the inequality |x - 7| > 2 without absolute value bars.
    x - 7 < -2 or x - 7 > 2.
  • Rewrite the inequality |x + 3| < 7 without absolute value bars.
    -7 < x + 3 < 7.