Question 1

Which of the following is the correct first step to solve the linear equation $$3(2 - 5x) = 4x + 25$$?

Accepted Answer

Distribute the constant $$3 to $$both terms inside the parentheses.

Question 2

After distributing in the equation $$3(2 - 5x) = 4x + 25$$, what is the resulting equation?

Accepted Answer

$$6 - 15x = 4x + 25$$

Question 3

What is the solution to the equation $$3(2 - 5x) = 4x + 25$$?

Accepted Answer

Question 4

When solving linear equations with fractions, what is the most effective first step?

Accepted Answer

Multiply both sides by the least common denominator.

Question 5

Solve the equation $$\frac{1}{4}(x + 2) - \frac{1}{3}x = \frac{1}{12}. $$What is the value of $$x$$?

Accepted Answer

$$x = 2$$

Question 6

Which step should be performed after distributing constants when solving a linear equation?

Accepted Answer

Combine like terms.

Question 7

A linear equation is categorized based on the number of solutions it has. Which of the following is NOT a possible category?

Accepted Answer

Two solutions

Question 8

If you solve a linear equation and end up with a statement like $$0 = 0$$, what does this indicate about the equation?

Accepted Answer

The equation has infinite solutions.

Question 9

In the equation $$2(x - 3) = 0$$, what is the solution for $$x$$?

Accepted Answer

$$x = 3$$

Question 10

After solving a linear equation, why is it important to check the solution by substituting back into the original equation?

Accepted Answer

To ensure the solution satisfies the original equation.

Question 11

Which of the following best describes the process of isolating $$x in a $$linear equation?

Accepted Answer

Moving all terms with $$x to $$one side and constants to the other.

Question 12

A medical researcher models the dosage of a drug with the equation $$5d + 10 = 35. $$What is the correct dosage $$d$$?

Accepted Answer

$$d = 5$$

Question 13

Which step is necessary to solve the equation $$\frac{1}{2}x + \frac{1}{3} = \frac{5}{6}$$?

Accepted Answer

Multiply both sides by $$6 to $$eliminate fractions.

Question 14

A chemical reaction is modeled by $$4c - 7 = 9. $$What is the concentration $$c$$?

Accepted Answer

$$c = 2$$

Question 15

If you solve a linear equation and end up with a statement like $$5 = 0$$, what does this indicate?

Accepted Answer

The equation has no solution.

Question 16

Which of the following is a multi-step process for solving linear equations with fractions?

Accepted Answer

Multiply by the least common denominator, distribute constants, combine like terms, group $$x$$ and constants, isolate $$x$$, check solution.

Question 17

A historian models the number of artifacts found with $$2a + 5 = 17. $$What is the value of $$a$$?

Accepted Answer

$$a = 6$$

Question 18

Which of the following is NOT a step in solving linear equations?

Accepted Answer

Factor quadratic expressions

Question 19

A real-world scenario: A phone plan charges $$20$$ per month plus $$5$$ per gigabyte of data. If your bill is $$45$$, how many gigabytes did you use?

Accepted Answer

$$5$$

Question 20

Which of the following best describes a linear equation?

Accepted Answer

An equation where the highest power of the variable is $$1$$

Solving Linear Equations: Methods and Applications

Study Guide - Practice Questions