Grade 7 Linear Equations Test PDF
Free preview of a printable Grade 7 Linear Equations test with a complete step-by-step answer key. Common Core 7.EE aligned · balanced 5/3/2 difficulty.
1. Solve: x + 6 = 21
2. Solve: 4x = 28
3. Solve: x/3 = 6
4. Solve: 5x + 3 = 23
5. Solve: 3x − 4 = 11
6. Solve: 6x + 1 = 4x + 15
7. Solve: 2(x − 3) = 10
8. Solve: (x + 4)/2 = 7
9. Solve: 3(2x − 1) = 4x + 9
10. A number tripled and decreased by 5 equals 28. Find the number.
1. x = 15
x = 21 − 6 = 15
2. x = 7
x = 28 ÷ 4 = 7
3. x = 18
x = 6 × 3 = 18
4. x = 4
5x = 20 → x = 4
5. x = 5
3x = 15 → x = 5
6. x = 7
2x = 14 → x = 7
7. x = 8
x − 3 = 5 → x = 8
8. x = 10
x + 4 = 14 → x = 10
9. x = 6
6x − 3 = 4x + 9 → 2x = 12 → x = 6
10. x = 11
3x − 5 = 28 → 3x = 33 → x = 11
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Topics covered
One- and two-step equations, equations with variables on both sides, word problems.
Difficulty balance
5 easy / 3 medium / 2 hard — fair grading across abilities.
Answer key
Step-by-step solutions for every question.
What the answer key covers
The worked answer key shows the inverse operation used at each step, so teachers can review the reasoning rather than checking final answers only.
One-step equations
Undo addition, subtraction, multiplication, or division while keeping both sides equal.
Two-step equations
Simplify in a deliberate order and show how the variable is isolated.
Variables on both sides
Collect variable terms on one side and constants on the other.
Word problems
Translate the situation into an equation, solve it, and interpret the result.