Question 1

Which of the following best describes a linear equation in one variable?

Accepted Answer

An equation that can be written in the form $$ax + b = 0$$ where $$a$$ and $$b$$ are integers and $$x is a $$variable.

Question 2

Solve for $$x$$: $$-2x + 7 = 8$$

Accepted Answer

Question 3

Which property of equality justifies the step from $$a = b to$$ $$a + c = b + c$$?

Accepted Answer

Addition Property of Equality

Question 4

Solve for $$x$$: $$8 + 5x = 7(x - 4)$$

Accepted Answer

$$x = 8$$

Question 5

Which of the following equations is an identity?

Accepted Answer

$$2x + 4 = 2(x + 2)$$

Question 6

Solve for $$x$$: $$\frac{3}{4} + x = \frac{1}{2}x - \frac{1}{2}$$

Accepted Answer

$$x = -2$$

Question 7

Which of the following best describes an inconsistent equation?

Accepted Answer

An equation that has no solution.

Question 8

Solve for $$x$$: $$4(x - 6) = 4x - 24$$

Accepted Answer

All real numbers

Question 9

Which equation below is a conditional equation?

Accepted Answer

$$x + 5 = 10$$

Question 10

Solve for $$x$$: $$\frac{x}{x+1} + \frac{2}{x-1} = 1$$

Accepted Answer

$$x = 3$$

Question 11

Which property of equality is used when both sides of an equation are divided by the same nonzero number?

Accepted Answer

Division Property of Equality

Question 12

Solve for $$x$$: $$5(x - 10) = 5x - 40$$

Accepted Answer

All real numbers

Question 13

Solve for $$x$$: $$\frac{2}{x} + \frac{3}{x+1} = 5$$

Accepted Answer

Question 14

If $$|x + 3| = 8$$, what are the solutions for $$x$$?

Accepted Answer

$$x = 11 or$$ $$x = -5$$

Question 15

A carpenter used 45 ft in three pieces to trim a garage door. If the long piece was 5 ft longer than twice the length of each shorter piece, what is the length of each shorter piece?

Accepted Answer

7 ft

Question 16

Sam and his friend James bought a used car for $27,540, including sales tax. If the sales tax rate is 8%, what was the cost of the car before the sales tax?

Accepted Answer

$$25,500$$

Question 17

If a circular race track is 1.8 mi in circumference and is to be built in a square plot of land, what is the minimum number of acres needed? (1 acre = 43,560 ft$$^2)$$

Accepted Answer

About 16.5 acres

Question 18

Solve for $$x$$: $$3|x + 5| - 9 = 0$$

Accepted Answer

$$x = -2 or$$ $$x = -8$$

Question 19

Which of the following is the correct solution set for $$|x - 8| = 12$$?

Accepted Answer

$$x = 20 or$$ $$x = -4$$

Equations in One Variable: Precalculus Study Notes

Study Guide - Practice Questions

Study Guide - Flashcards