Solving Linear Equations: Grade 8 Math Test – PDF Download

Question 1: Multi-step equations (2 points)

Solve each equation.

1. \(5x-7=18\) (1 point)
2. \(3(x-4)=-21\) (1 point)

Question 2: Variables on both sides (3 points)

Solve each equation.

1. \(6x+5=2x+25\) (1 point)
2. \(4(x-2)=x+10\) (1 point)
3. \(3(2x+1)-4x=19\) (1 point)

Question 3: Fractions and decimals (3 points)

Solve each equation.

1. \(\frac{2}{5}x+3=11\) (1 point)
2. \(1.2x-0.5=0.7x+2\) (1 point)
3. \(\frac{1}{3}(x+6)=\frac{1}{2}x-1\) (1 point)

Question 4: Number of solutions (3 points)

For each equation, state whether it has one solution, no solution or infinitely many solutions. Solve if it has one solution.

1. \(5x+2(x-1)=7x-2\) (1 point)
2. \(3(x+4)=3x+9\) (1 point)
3. \(6x-4=2(x+2)\) (1 point)

Question 5: Choose the constant (2 points)

Consider the equation \(3(x+2)=3x+k\).

1. Find the value of \(k\) that gives infinitely many solutions. (1 point)
2. Give one value of \(k\) that gives no solution. (1 point)

Question 6: Equal perimeters (2 points)

The rectangle and the square shown have the same perimeter. Write an equation and tell how many values of \(x\) make this true. Explain.

Question 7: Savings plans (3 points)

The table shows two savings plans.

1. Write an expression for each person’s total after \(w\) weeks. (1 point)
2. After how many weeks do they have the same total? (1 point)
3. How much do they each have then? (1 point)

Question 8: Find the error (2 points)

Noah’s work is shown. Find his mistake and give the correct solution.

⬇ Download the Grade 8 Solving Linear Equations test (PDF, 84 KB)

See every chapter on the Grade 8 math page.