Question 1

Which of the following is a linear equation?

Accepted Answer

$$2x + 3 = 5$$

Question 2

Solve for $$x$$: $$2x + 3 = 11$$

Accepted Answer

$$x = 4$$

Question 3

Which operation should you perform first to solve $$3(2 - 5x) = 4x + 25$$?

Accepted Answer

Distribute the 3 to both terms inside the parentheses

Question 4

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

Accepted Answer

$$x = -1$$

Question 5

A chemist is mixing two solutions. The equation $$5x + 17 = 8x + 12 - 3(x + 4)$$ models the total amount of a chemical in the mixture. What is the value of $$x$$?

Accepted Answer

$$x = 3$$

Question 6

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

Accepted Answer

$$x + 5 = x + 5$$

Question 7

Solve for $$x$$ and state the type of solution: $$x + 4 = x + 4$$

Accepted Answer

Identity; infinite solutions

Question 8

Solve for $$x$$ and state the type of solution: $$x + 2 = x + 3$$

Accepted Answer

Inconsistent; no solution

Question 9

A medical researcher is tracking the dosage of a drug in the bloodstream. The equation $$\frac{1}{4}x + \frac{1}{6} = \frac{x}{3}$$ models the concentration. What is the value of $$x$$?

Accepted Answer

$$x = 1.2$$

Question 10

Which step is NOT part of the standard process for solving a linear equation?

Accepted Answer

Multiply both sides by a variable

Question 11

Solve for $$x$$: $$2(x - 3) = 0$$

Accepted Answer

$$x = 3$$

Question 12

A business has a profit modeled by $$4x - 2 = 2x + 10. $$What is the value of $$x$$ when the profit is balanced?

Accepted Answer

$$x = 6$$

Question 13

Which of the following best describes a conditional equation?

Accepted Answer

An equation that is true for only one value of the variable

Question 14

Solve for $$x$$: $$-2(5 - 3x) + x = 7x - 10$$

Accepted Answer

$$x = 1.5$$

Question 15

Which of the following equations is inconsistent?

Accepted Answer

$$x + 2 = x + 3$$

Question 16

A recipe calls for $$\frac{1}{2}$$ cup of sugar plus $$x$$ cups of flour to equal $$2$$ cups. What is the value of $$x$$?

Accepted Answer

$$x = 1.5$$

Question 17

Which of the following is the correct first step to solve $$\frac{1}{2}(x + 2) - \frac{1}{3}x = \frac{1}{2}$$?

Accepted Answer

Multiply both sides by 6 to eliminate fractions

Question 18

If a linear equation simplifies to $$0 = 0$$, what type of equation is it?

Accepted Answer

Identity

Question 19

Solve for $$x$$: $$2x - 6 = 2x + 1$$

Accepted Answer

Inconsistent; no solution

Question 20

A student solves $$3x + 2 = 3x + 2$$ and concludes there is only one solution. What is the error?

Accepted Answer

The equation is an identity and has infinite solutions

Solving Linear Equations: Concepts, Methods, and Classification

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