Question 1

Solve the equation $$2(x - 3) = 4x + 6$$ for $$x.$$

Accepted Answer

Question 2

Solve the equation $$\frac{2x}{3} - \frac{5}{6} = \frac{x}{2} + 1$$ for $$x.$$

Accepted Answer

$$x = 6$$

Question 3

Which of the following equations is an identity (true for all real numbers)?

Accepted Answer

$$2x + 5 = 2x + 5$$

Question 4

Solve the equation $$0.3x + 2.1 = 0.5x - 1.3$$ for $$x.$$

Accepted Answer

$$x = 17$$

Question 5

Which of the following equations has no solution?

Accepted Answer

$$4x + 7 = 4x - 2$$

Question 6

A chemist needs to prepare 100 mL of a 30% saline solution by mixing a 20% solution and a 50% solution. Let $$x be $$the amount (in mL) of the 20% solution used. Which equation models this scenario?

Accepted Answer

$$0.2x + 0.5(100 - x) = 30$$

Question 7

Solve for $$x$$: $$\frac{3x - 2}{4} = \frac{x + 6}{2}.$$

Accepted Answer

$$x = 5$$

Question 8

If $$3(x - 2) + 4 = 2x + 7$$, what is the value of $$x$$?

Accepted Answer

$$x = 6$$

Question 9

Which of the following best describes the equation $$5x + 2 = 5x - 3$$?

Accepted Answer

It has no solution.

Question 10

A medical researcher models the relationship between stress level $$S$$ and hours of sleep $$h as$$ $$S = 20 - 2h. If a $$patient reports a stress level of 12, how many hours of sleep did they get?

Accepted Answer

$$h = 6$$

Question 11

Solve for $$x$$: $$0.6x - 1.2 = 0.2x + 2.8.$$

Accepted Answer

$$x = 10$$

Question 12

Which of the following is the first step in solving the equation $$\frac{2x + 3}{5} = 4$$?

Accepted Answer

Multiply both sides by 5.

Question 13

If $$x is a $$solution to $$7x + 2 = 3x + 18$$, what is the value of $$x$$?

Accepted Answer

$$x = 4$$

Question 14

A car rental company charges a flat fee of $$\25$ plus $$\$$0.20$$ per mile driven. If the total cost for a trip was $$\61$, how many miles were driven?

Accepted Answer

$$180$$

Question 15

Solve for $$x$$: $$\frac{1}{2}x + \frac{1}{3} = \frac{5}{6}.$$

Accepted Answer

$$x = 2$$

Linear Equations and Inequalities in One Variable: Study Guide

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