Solving simple equations: Class 7 practice
An equation is a balance: whatever you do to one side you must do to the other. Read the method, follow the three worked examples, then try the six questions.
What you should know first
- Integers
- Inverse operations
The idea behind solving simple equations
An equation is a balance: whatever you do to one side you must do to the other. Undo operations in reverse order — remove the added/subtracted number first, then divide.
Step-by-step method
- Move the constant term by doing the opposite operation on both sides.
- Divide both sides by the coefficient of x.
- Substitute back to check.
Worked example 1 (Basic)
Solve: 2x + 2 = 8
- 2x = 8 − 2 = 6
- x = 6 ÷ 2 = 3
- Check: 2(3) + 2 = 8 ✓
- Answer: x = 3
Worked example 2 (Standard)
Solve: 12x − 15 = -87
- 12x = -87 + 15 = -72
- x = -72 ÷ 12 = -6
- Check: 12(-6) − 15 = -87 ✓
- Answer: x = -6
Worked example 3 (Challenge)
Solve: (12x + 18) / 4 = -18/4
- Multiply both sides by 4: 12x + 18 = -18
- 12x = -36
- x = -3
- Check: 12(-3) + 18 = -18 ✓
- Answer: x = -3
Common mistakes and misconceptions
- Changing the sign on only one side
- Dividing only one term instead of the whole side
Practice questions
- (Basic) Solve: 4x + 11 = -5
- (Basic) Solve: 2x + 24 = 16
- (Standard) Solve: 12x + 5 = 77
- (Standard) Solve: 5x − 7 = -52
- (Challenge) Solve: (12x + 18) / 5 = 198/5
- (Challenge) Solve: (4x + 18) / 5 = 26/5
Answer key with full working
- Q1: 4x = -5 − 11 = -16 → x = -16 ÷ 4 = -4 → Check: 4(-4) + 11 = -5 ✓ → Answer: x = -4
- Q2: 2x = 16 − 24 = -8 → x = -8 ÷ 2 = -4 → Check: 2(-4) + 24 = 16 ✓ → Answer: x = -4
- Q3: 12x = 77 − 5 = 72 → x = 72 ÷ 12 = 6 → Check: 12(6) + 5 = 77 ✓ → Answer: x = 6
- Q4: 5x = -52 + 7 = -45 → x = -45 ÷ 5 = -9 → Check: 5(-9) − 7 = -52 ✓ → Answer: x = -9
- Q5: Multiply both sides by 5: 12x + 18 = 198 → 12x = 180 → x = 15 → Check: 12(15) + 18 = 198 ✓ → Answer: x = 15
- Q6: Multiply both sides by 5: 4x + 18 = 26 → 4x = 8 → x = 2 → Check: 4(2) + 18 = 26 ✓ → Answer: x = 2
Syllabus note
This skill is listed under "Simple Equations" for Class 7 in the NCERT/CBSE books. ICSE, IGCSE, IB and state boards may teach it in a different chapter or year.
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.
Related practice and notes
Frequently asked questions
Which chapter is solving simple equations in?
"Simple Equations", Class 7 Maths (NCERT/CBSE). Other boards may place it differently.
How were the answers checked?
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.