$$x = \frac{7}{6 - 7} = -7$$, restriction: $$x \neq 1$$

Question 1

Which of the following points is located in Quadrant II of the rectangular coordinate system?

Accepted Answer

$$(-4, 5)$$

Question 2

What is the solution to the linear equation $$3(2 - 5x) = 4x + 25$$?

Accepted Answer

$$x = 1$$

Question 3

Solve the linear equation with fractions: $$\frac{1}{2}(x + 2) - \frac{1}{3}x = \frac{1}{12}.$$

Accepted Answer

$$x = -2$$

Question 4

Which of the following equations is an identity (true for all real numbers)?

Accepted Answer

$$x + 5 = x + 2 + 3$$

Question 5

Solve the rational equation $$\frac{x}{x-1} = \frac{7}{6}$$ and state any restrictions.

Accepted Answer

$$x = \frac{7}{6 - 7} = -7$$, restriction: $$x 
eq 1$$

Question 6

What is the simplified form of $$\sqrt{-75}$$?

Accepted Answer

$$5i\sqrt{3}$$

Question 7

Which of the following is the correct value for $$i^{22}$$?

Accepted Answer

$$-1$$

Question 8

Express $$9 + \sqrt{-16} in $$standard complex form.

Accepted Answer

$$9 + 4i$$

Question 9

Find the sum of the complex numbers $$5(4 + 7i) + 6(3 - 2i)$$ and express your answer in standard form.

Accepted Answer

$$38 + 29i$$

Question 10

Multiply the complex numbers $$2(i9 - 4i)(6 + 5i)$$ and express your answer in standard form.

Accepted Answer

$$2(9 - 4i)(6 + 5i) = 2(54 + 45i - 24i - 20i^2$) = 2(54 + 21i + 20) = 2(74 + 21i) = 148 + 42i$$

Question 11

Which of the following is a restriction for the rational equation $$\frac{x+4}{x-1} = 5$$?

Accepted Answer

$$x 
eq 1$$

Question 12

If $$i = \sqrt{-1}$$, what is the value of $$i^{100}$$?

Accepted Answer

$$1$$

Question 13

Which of the following is the standard form of a complex number?

Accepted Answer

$$a + bi$$

Question 14

What is the solution set for the equation $$x = x + 4$$?

Accepted Answer

No solution

Question 15

Which operation is necessary to isolate $$x in $$the equation $$x + 7 = 0$$?

Accepted Answer

Subtract 7 from both sides

Question 16

What is the solution to the equation $$\frac{5}{x} = \frac{4}{3x} + \frac{3}{x}$$?

Accepted Answer

$$x = 4$$

Question 17

Simplify $$\sqrt{-32}.$$

Accepted Answer

$$4i\sqrt{2}$$

Question 18

Which of the following is true about the square root of a negative number?

Accepted Answer

It is an imaginary number

Question 19

What is the result of $$(3 + 8i)^2$ in standard form?

Accepted Answer

$$-55 + 48i$$

College Algebra Study Guide: Linear Equations, Rational Equations, and Complex Numbers

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