Linear Equations Test – Grade 8 Math (Printable PDF)

Question 1 Variables on both sides (2 points)

Solve 7x − 12 = 3x + 20.

Question 2 Parentheses (3 points)

Solve 4(2x − 3) = 3(x + 6).

Question 3 Fractions (3 points)

Solve 25x + 3 = 15x + 7.

Question 4 Match the picture (3 points)

Panels A, B and C show the two sides of an equation as lines. Match each equation to a panel and state the number of solutions. (1 point each)

1. 6x + 9 = 3(2x + 3)
2. 8x − 5 = 8x + 1
3. 2x + 11 = 5x − 1

Question 5 Frame perimeter (3 points)

A rectangular picture frame has length 2x + 1 inches and width x + 3 inches. The perimeter is 50 inches. Write an equation (1 point), solve it (1 point) and give the length and width (1 point).

Question 6 Streaming plans (3 points)

Plan A costs a $30 setup fee plus $12 per month. Plan B costs a $6 setup fee plus $15 per month. After how many months are the total costs equal (2 points), and what is that total (1 point)?

Question 7 Find Dev’s error (2 points)

Dev solved 3(x + 4) = 2x + 20 and wrote 3x + 4 = 2x + 20, so x = 16. Find his mistake and give the correct solution.

Question 8 Choosing k (1 point)

Find k so that 5x + 2 = kx + 9 has no solution.