Question 1

Which of the following is a linear equation?

Accepted Answer

$$2x + 3 = 0$$

Question 2

What is the first step when solving the equation $$2(x - 4) = 10$$?

Accepted Answer

Apply the distributive property

Question 3

If $$3x + 5 = 20$$, what is the value of $$x$$?

Accepted Answer

Question 4

Which operation must be applied to both sides of a linear equation to maintain equality?

Accepted Answer

Any operation (addition, subtraction, multiplication, division)

Question 5

Given the equation $$2x - 6 + 3x = 5x - 6$$, what is the next step after combining like terms?

Accepted Answer

Move all terms with $$x to $$one side

Question 6

A chemist mixes a solution such that the equation $$4x + 2 = 18$$ models the amount of a chemical in grams. What is the amount of chemical, $$x$$, in grams?

Accepted Answer

$$x = 5$$

Question 7

Which of the following is NOT a linear expression?

Accepted Answer

$$x^2 + 1$

Question 8

If $$2(x + 3) = 14$$, what is the value of $$x$$ after distributing and solving?

Accepted Answer

$$x = 4$$

Question 9

A medical researcher uses the equation $$5x - 10 = 0 to $$model a dosage. What is the correct dosage, $$x$$?

Accepted Answer

$$x = 2$$

Question 10

Which step is necessary to solve $$3(x - 2) = 9$$?

Accepted Answer

Apply the distributive property

Question 11

A business calculates profit using $$2x + 100 = 500. $$What is the value of $$x$$?

Accepted Answer

$$x = 200$$

Question 12

Which of the following best describes a linear equation?

Accepted Answer

An equation where the variable is raised to the first power

Question 13

If $$x + 2 = 0$$, what is the value of $$x$$?

Accepted Answer

$$x = -2$$

Question 14

Which property allows you to write $$2(x - 3) as$$ $$2x - 6$$?

Accepted Answer

Distributive property

Question 15

A historian analyzes data using $$x + 50 = 120. $$What is the value of $$x$$?

Accepted Answer

$$x = 70$$

Linear Equations: Definitions, Concepts, and Solution Steps

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