Question 1

Solve the equation $$5x + 12 = 2x - 4. $$What is the value of $$x$$?

Accepted Answer

$$x = -rac{16}{3}$$

Question 2

Which of the following is the solution set for the inequality $$2x - 5 \u003c 3x + 1 in $$interval notation?

Accepted Answer

$$(-6, \infty)$$

Question 3

Simplify the expression $$\sqrt{50} - 2\sqrt{2}.$$

Accepted Answer

$$5\sqrt{2} - 2\sqrt{2} = 3\sqrt{2}$$

Question 4

Which equation can be solved using the zero-factor property?

Accepted Answer

$$x^2 + 5x = 0$

Question 5

Solve the quadratic equation $$x^2 - 6x + 9 = 0$ by factoring.

Accepted Answer

$$x = 3$$

Question 6

Which of the following numbers is a pure imaginary number?

Accepted Answer

$$-3i$$

Question 7

Write the product of $$\sqrt{-9}$$ and $$\sqrt{-4} in $$the form $$a + bi.$$

Accepted Answer

$$-6$$

Question 8

Solve for $$x$$: $$\frac{2x}{3} - 4 = 8$$

Accepted Answer

$$x = 18$$

Question 9

Which of the following equations has no real solution?

Accepted Answer

$$x^2 + 4 = 0$

Question 10

Solve the equation $$x^2 = 25$ using the square root property.

Accepted Answer

$$x = \pm 5$$

Question 11

Given the quadratic equation $$x^2 - 2x + 1 = 0$, how many distinct real solutions does it have?

Accepted Answer

One distinct real solution

Question 12

Which of the following is the correct interval notation for the solution set of $$x \u003e -3$$?

Accepted Answer

$$(-3, \infty)$$

Question 13

Simplify the expression $$\frac{2 + 3i}{1 - i}$$ and write your answer in the form $$a + bi.$$

Accepted Answer

Question 14

Which of the following is the solution set for the inequality $$3x + 2 \leq 8$$?

Accepted Answer

$$(-\infty, 2]$$

Question 15

Solve the equation $$x^2 + 4x + 4 = 0$ using the quadratic formula.

Accepted Answer

$$x = -2$$

Question 16

If $$a = 2 + 3i$$ and $$b = 1 - 2i$$, what is $$a + b$$?

Accepted Answer

$$3 + i$$

Question 17

Which of the following is the solution set for $$|x - 4| \u003c 3$$?

Accepted Answer

$$(1, 7)$$

Question 18

Evaluate the discriminant for the equation $$x^2 + 2x + 5 = 0$ and determine the nature of its solutions.

Accepted Answer

The equation has two distinct complex solutions.

Question 19

Which of the following is the correct solution for $$\sqrt{x^2$} = 7$$?

Accepted Answer

$$x = \pm 7$$

Question 20

Which of the following is the solution set for the inequality $$x^2 - 4$$ \u003c 0$$?

Accepted Answer

$$(-2, 2)$$

College Algebra: Equations, Inequalities, and Complex Numbers Study Guide

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