$$x = 3$$; restriction: $$x \neq 1$$

Question 1

Which of the following is the correct solution to the linear equation $$3(2 - 5x) = 4x + 25$$?

Accepted Answer

$$x = -1.5$$

Question 2

What is the solution set for the equation $$x + 5 = x + 2 + 3$$?

Accepted Answer

All real numbers

Question 3

Solve the rational equation $$\frac{2x+4}{x-1} = 5. $$What is the restriction on $$x$$?

Accepted Answer

$$x = 3$$; restriction: $$x 
eq 1$$

Question 4

Simplify $$\sqrt{-75}$$ using the imaginary unit.

Accepted Answer

$$5i\sqrt{3}$$

Question 5

What is $$i^{22}$$?

Accepted Answer

$$1$$

Question 6

Identify the real and imaginary parts of the complex number $$4 - 3i.$$

Accepted Answer

Real: $$4$$, Imaginary: $$-3$$

Question 7

Find the sum $$(4 + 8i) + (2 + 3i)$$ and express your answer in standard form.

Accepted Answer

$$6 + 11i$$

Question 8

Multiply $$(2 + 3i)(2 - 3i). $$What is the result?

Accepted Answer

$$13$$

Question 9

Divide $$\frac{6 + i}{4 - 2i}$$ and express your answer in standard form.

Accepted Answer

$$1 + \frac{1}{2}i$$

Question 10

Which method is best to solve the quadratic equation $$(x + 2)^2$ = 9$$?

Accepted Answer

Square root property

Question 11

Write $$-4x^2 + x = 8$ in standard form and identify a$, b$, and c$.

Accepted Answer

$$a = -4$$, $$b = 1$$, $$c = -8$$

Question 12

Solve $$2x^2 + 7x + 6 = 0$ by factoring.

Accepted Answer

$$x = -2$$, $$x = -3$$

Question 13

Use the quadratic formula to solve $$3x^2 + 4x + 1 = 0$.

Accepted Answer

$$x = -1$$, x = -\frac{1}{3}$

Question 14

Determine the number and type of solutions for $$x^2 + 8x + 16 = 0$ using the discriminant.

Accepted Answer

One real solution

Question 15

Express the set $$\{x | 0 \u003c x \u003c 5\} in $$interval notation.

Accepted Answer

$$(0, 5)$$

Question 16

Solve the inequality $$2x + 12 \u003e 19$$ and express the solution in interval notation.

Accepted Answer

$$(3.5, \infty)$$

Question 17

What happens to the inequality symbol when you multiply or divide both sides by a negative number?

Accepted Answer

It reverses direction

Question 18

Solve the inequality $$\frac{1}{3}(x+1) \geq \frac{1}{5}(3+2x)$$ and express the solution in interval notation.

Accepted Answer

$$[2, \infty)$$

Question 19

A quadratic equation $$ax^2 + bx + c = 0$ has a negative discriminant. What does this mean?

Accepted Answer

It has two imaginary solutions

College Algebra: Equations, Inequalities, and Quadratic Equations Study Guide

Study Guide - Practice Questions