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

1 Warm-up: one and two steps / 4 pts

No calculator. Solve each equation.

1. \(2x - 9 = 7\)
2. \(-3y + 5 = -10\)
3. \(\dfrac{m}{5} + 2 = -1\)
4. \(7 = 2(p - 3) + 1\)

2 Variables on both sides / 4 pts

Solve each equation and check your answer.

1. \(6x + 1 = 2x + 17\)
2. \(5(2n - 1) = 3(3n + 2)\)

3 Fractions and decimals / 3 pts

Solve each equation.

1. \(\dfrac{2x}{3} - \dfrac{1}{2} = \dfrac{x}{6} + 1\)
2. \(0.5x + 0.25 = 2.75\)

4 How many solutions? / 3 pts

Decide whether each equation has one solution, no solution, or infinitely many. Give the solution when there is exactly one.

1. \(5x - 2 = 5(x - 1) + 3\)
2. \(3(2x + 1) = 6x + 5\)
3. \(4x + 7 = 2x - 1\)

5 Print shop / 3 pts

Calculator allowed. Shop A charges a $6 setup fee plus $0.20 per page. Shop B has no setup fee and charges $0.35 per page. Write an equation, find the number of pages for which both shops cost the same, and give that cost.

6 Consecutive even integers / 3 pts

The sum of three consecutive even integers is 90. Find them.