Solving Linear Equations: math practice, Grade 8 – download the PDF

1 Undo a subtraction ★★★

Solve \(y - 7 = 12\) and check your answer.

2 Negative coefficient ★★★

Solve \(-4a = 36\).

3 A basic two-step equation ★★★

Solve \(3x + 8 = 26\).

4 Dividing first ★★★

Solve \(\dfrac{x}{4} - 3 = 2\).

5 Subtracting from a number ★★★

Solve \(6 - 2k = 18\).

6 Is it a solution? ★★★

Is \(x = -3\) a solution of \(5x + 7 = 2x - 2\)? Show your work.

7 Taxi ride ★★★

A taxi charges a $3.50 pickup fee plus $2 for each mile. Maria’s ride cost $15.50. Write an equation and find how many miles she rode.

8 Opening parentheses ★★★

Solve \(4(x - 3) = 28\) in two different ways: first by dividing by 4, then by distributing.

9 Like terms first ★★★

Solve \(3x + 4x - 9 = 19\).

10 The variable on both sides ★★★

Solve \(9x - 5 = 4x + 20\).

11 A minus sign before parentheses ★★★

Solve \(6 - 3(x + 1) = 15\).

12 Find the error ★★★

Jon solves \(2x + 1 = 2x + 3\). He subtracts \(2x\) from both sides, gets \(1 = 3\), and writes “\(x = 1\)”. Explain what is wrong and give the correct conclusion.

13 Equation with a fraction bar ★★★

Solve \(\dfrac{2x - 1}{5} = 3\).

14 Garden perimeter ★★★

A rectangular garden is 3 feet longer than it is wide, and its perimeter is 46 feet (about 14 meters). Use the figure to write an equation, then find the width and the length.

15 Fahrenheit and Celsius ★★★

The formula \(F = 1.8C + 32\) converts degrees Celsius to degrees Fahrenheit. On a hot day a thermometer reads \(95^\circ\text{F}\). What is the temperature in degrees Celsius?

16 Distribute on both sides ★★★

Solve \(5(2x - 3) - 4x = 3(x + 4) + 6\).

17 Fractions on both sides ★★★

Solve \(\dfrac{3}{4}x + 2 = \dfrac{1}{4}x + \dfrac{7}{2}\).

18 Decimals and parentheses ★★★

Solve \(0.6(x - 5) = 0.2x + 1\).

19 How many solutions? ★★★

Consider the equation \(2(x + 3) = 2x + c\), where \(c\) is a number.

1. For which value of \(c\) does it have infinitely many solutions?
2. For which values of \(c\) does it have no solution?
3. Can it ever have exactly one solution? Explain.

20 Bike rental showdown ★★★

Shop A rents a bike for $12 plus $4 per hour. Shop B charges $4 plus $6 per hour. After how many hours do the two shops cost the same, and what is that cost? Write an equation and solve it.

21 Consecutive integers ★★★

The sum of three consecutive integers is 9 less than 4 times the smallest one. Find the three integers.

22 Fractions of expressions ★★★

Solve \(\dfrac{x - 1}{2} = \dfrac{x + 3}{4} + 1\).