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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