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

Question 2

What is the solution to the equation $$2(x - 3) = 0$$?

Accepted Answer

$$x = 3$$

Question 3

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

Accepted Answer

Multiply both sides by the least common denominator.

Question 4

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

Accepted Answer

$$x = 3$$

Question 5

After distributing and combining like terms, which equation is equivalent to $$3(2 - 5x) = 4x + 25$$?

Accepted Answer

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

Question 6

Which step should be performed after grouping terms with $$x$$ and constants on opposite sides when solving a linear equation?

Accepted Answer

Isolate $$x$$

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

Solve and categorize the equation $$4x + 8 = 4(x + 2). $$What type of solution does it have?

Accepted Answer

Infinite solutions

Question 9

Which of the following best describes the process of checking a solution to a linear equation?

Accepted Answer

Replace $$x in $$the original equation and verify both sides are equal.

Question 10

A medical researcher models the dosage of a drug with the equation $$5d + 10 = 25. $$What is the correct dosage $$d$$?

Accepted Answer

$$d = 3$$

Question 11

If a chemical reaction is modeled by $$2c - 4 = 10$$, what is the value of $$c$$?

Accepted Answer

$$c = 7$$

Question 12

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

Accepted Answer

Multiply both sides by $$10 to $$eliminate fractions.

Question 13

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

Accepted Answer

$$x = 6.25$$

Question 14

A historical event is modeled by the equation $$y - 1945 = 75. $$What year does $$y$$ represent?

Accepted Answer

$$y = 2020$$

Question 15

Which of the following equations has no solution?

Accepted Answer

$$2x + 3 = 2x + 5$$

Question 16

If a linear equation is written as $$ax + b = cx + d$$, what is the next step after distributing and combining like terms?

Accepted Answer

Group terms with $$x$$ and constants on opposite sides.

Question 17

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

Accepted Answer

$$5$$

Question 18

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

Accepted Answer

Multiply both sides by $$x.$$

Question 19

If a linear equation has infinite solutions, what does this mean about the equation?

Accepted Answer

Both sides are equivalent for all values of $$x.$$

Question 20

Solve the equation $$6x - 2 = 4x + 10$$ and select the correct solution.

Accepted Answer

$$x = 6$$

Solving Linear Equations: Methods and Applications

Study Guide - Practice Questions