$$x = 2$$, 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

$$x = -1$$

Question 2

What is the least common denominator (LCD) needed to solve the equation $$\frac{1}{4}(x+2) - \frac{1}{3}x = \frac{1}{12}$$?

Accepted Answer

$$12$$

Question 3

Which category does the equation $$x = x + 4$$ fall into?

Accepted Answer

Inconsistent equation

Question 4

What is the standard form of a complex number?

Accepted Answer

$$a + bi$$

Question 5

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

Accepted Answer

$$6 + 11i$$

Question 6

What is the product of $$(2 + 3i)(2 - 3i)$$?

Accepted Answer

$$13$$

Question 7

Simplify $$i^{22}.$$

Accepted Answer

$$1$$

Question 8

Which method is best to solve the quadratic equation $$x^2 - 5 = 0$?

Accepted Answer

Square root property

Question 9

What are the solutions to $$x^2 - 9x = -20$ after factoring?

Accepted Answer

$$x = -4, x = 5$$

Question 10

What is the discriminant of the equation $$x^2 + 8x + 16 = 0$ and what does it tell you about the solutions?

Accepted Answer

Discriminant is $$0$$, one real solution

Question 11

Which of the following points satisfies the equation $$x + y = 5$$?

Accepted Answer

$$(3, 2)$$

Question 12

What is the $$y-$$intercept of the equation $$y = 2x + 3$$?

Accepted Answer

$$3$$

Question 13

Solve the rational equation $$\frac{2x+4}{x-1} = 5$$ and state any restrictions.

Accepted Answer

$$x = 2$$, restriction $$x 
eq 1$$

Question 14

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

Accepted Answer

$$(0, 5)$$

Question 15

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

Accepted Answer

$$(3.5, \infty)$$

Question 16

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

Accepted Answer

It reverses

Question 17

Which of the following is the correct solution to $$\frac{1}{3}(x+1) \geq \frac{1}{5}(3+2x)$$?

Accepted Answer

$$x \geq 2$$

Question 18

What is the product of $$3i(7 - 2i)$$ expressed in standard form?

Accepted Answer

$$21i + 6$$

Question 19

What is the solution to $$y - x^2$ + 3 = 0$$ for $$x = 2$$?

Accepted Answer

$$y = 1$$

Question 20

Which method is best to solve $$x^2 + 3x - 5 = 0$?

Accepted Answer

Completing the square

College Algebra: Equations, Inequalities, and Complex Numbers

Study Guide - Practice Questions