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

The equation has two distinct complex solutions.

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 $2x - 5 < 3x + 1$ 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 $x > -3$?

Accepted Answer

$(-3, \infty)$

Question 13

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

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 $|x - 4| < 3$?

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 $x^2 - 4 < 0$?

Accepted Answer

$(-2, 2)$

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

Study Guide - Practice Questions