Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
Looking for a two-step equations test? Then this Grade 7 test on Solving Two-Step Equations with Rational Numbers checks the whole chapter, with points for each question. This test covers two-step equations of the forms px + q = r and p(x + q) = r with whole numbers, decimals, fractions and negatives, plus equations from diagrams and real situations. Show each step. Calculators are not allowed. Plan on 45 minutes for the 8 questions.
Standards: 7.EE.B.3, 7.EE.B.4a · Level: Grade 7
Question 1 Solve Two Equations (2 points)
Solve each equation.
- 6x + 9 = 51 (1 point)
- 4x − 11 = −35 (1 point)
Question 2 A Quotient Equation (2 points)
Solve x5 − 8 = −3.
Question 3 Decimal Coefficients (2 points)
Solve 3.2x + 1.6 = 14.4.
Question 4 Two Ways with Parentheses (3 points)
Consider 5(x − 2.4) = 16.
- Solve by dividing first. (1 point)
- Solve by distributing first. (1 point)
- Check the solution in the original equation. (1 point)
Question 5 Fractions in an Equation (3 points)
Solve 34(x + 23) = 72. Show every step.
Question 6 Equation from a Diagram (3 points)
The tape diagram shows three equal parts and one part of 7.5.
- Write an equation for the diagram. (1 point)
- Solve it. (1 point)
- Check the solution. (1 point)
Question 7 Gym Membership (3 points)
A gym charges a $35 sign-up fee plus $18.50 each month. Nia has paid $146 in total.
- Write an equation for the number of months m. (1 point)
- Solve the equation. (1 point)
- State what the solution means. (1 point)
Question 8 Find the Mistake (2 points)
Marcus’s work is shown.
- Identify his error. (1 point)
- Find the correct solution. (1 point)
