Free Equations Worksheets With Answers
These free equations worksheets progress from one-step equations through two-step equations to equations with brackets and variables on both sides, showing every line of working. Solving equations is the single most assessed skill in middle school algebra, and most errors come from one identifiable step rather than from the concept. The same skills can be generated as a printable equations test with a full answer key.
Grades 6–9 · 9 free questions with worked answers · No sign-up to practise
Skills covered in these equations worksheets
- One-step equations with addition and multiplication
- Two-step equations
- Equations with brackets
- Variables on both sides
- Equations involving fractions
- Forming an equation from a word problem
Free equations practice questions with answers
Every question below includes the final answer and the steps behind it, so the sheet doubles as its own answer key. Filter by grade or difficulty to build the set you need.
- Question 1easyGrade 6
Solve x + 7 = 12.
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Answer: x = 5
Subtract 7 from both sides: x = 12 − 7 = 5. Check: 5 + 7 = 12.
- Question 2easyGrade 6
Solve 4x = 28.
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Answer: x = 7
Divide both sides by 4: x = 28 ÷ 4 = 7. Check: 4 × 7 = 28.
- Question 3easyGrade 6
Solve x ÷ 3 = 9.
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Answer: x = 27
Multiply both sides by 3: x = 9 × 3 = 27. Check: 27 ÷ 3 = 9.
- Question 4mediumGrade 7
Solve 3x + 4 = 19.
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Answer: x = 5
Subtract 4 from both sides to get 3x = 15, then divide by 3 to get x = 5. Check: 3 × 5 + 4 = 19.
- Question 5mediumGrade 8
Solve 5x − 8 = 2x + 7.
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Answer: x = 5
Subtract 2x from both sides: 3x − 8 = 7. Add 8: 3x = 15. Divide by 3: x = 5.
- Question 6mediumGrade 8
Solve 2(x + 3) = 16.
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Answer: x = 5
Expand to 2x + 6 = 16, subtract 6 to get 2x = 10, then divide by 2 to get x = 5.
- Question 7hardGrade 9
Solve 4(x − 2) = 3(x + 1).
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Answer: x = 11
Expand both sides: 4x − 8 = 3x + 3. Subtract 3x: x − 8 = 3. Add 8: x = 11.
- Question 8hardGrade 9
Solve x/4 + 3 = 7.
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Answer: x = 16
Subtract 3 from both sides: x/4 = 4. Multiply both sides by 4: x = 16.
- Question 9hardGrade 9
A number is doubled and then 5 is subtracted, giving 17. What is the number?
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Answer: 11
Form the equation 2n − 5 = 17. Add 5 to get 2n = 22, then divide by 2 to get n = 11.
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Undo in the reverse order
To solve 3x + 4 = 19, undo the operations in the opposite order to how they were applied. The expression multiplies by 3 and then adds 4, so the solution subtracts 4 first and then divides by 3. Students who divide first must divide every term, including the 4, and most forget. Teaching the reverse-order rule explicitly removes the most common two-step error in one move.
Always check by substitution
Every equation carries its own answer key. Substituting the solution back into the original equation either balances or it does not, which means students never need to wait for a teacher to know whether they are right. Building this habit early is worth more than extra practice questions, because it turns solving into a self-correcting process rather than a guess.
Common mistakes to watch for
- Dividing before subtracting in a two-step equation, and dividing only part of the expression.
- Applying an operation to one side of the equation but not the other.
- Losing the sign when moving a negative term across the equals sign.
- Distributing over only the first term inside a bracket before solving.