Linear equations with the variable on both sides: Class 8 practice
Collect all x-terms on one side and all numbers on the other by transposing (changing sign as a term crosses the = sign).. Read the method, follow the three worked examples, then try the six questions.
What you should know first
- Simple equations
- Integers
The idea behind linear equations with the variable on both sides
Collect all x-terms on one side and all numbers on the other by transposing (changing sign as a term crosses the = sign).
Step-by-step method
- Transpose x-terms to the left, constants to the right.
- Simplify each side.
- Divide by the coefficient.
- Check by substitution in BOTH sides.
Worked example 1 (Basic)
Solve: 8x − 3 = 1x − 38
- 8x − 1x = -38 + 3
- 7x = -35
- x = -5
- Check: LHS = RHS = -43 ✓
- Answer: x = -5
Worked example 2 (Standard)
Solve: 6x + 3 = 5x + 9
- 6x − 5x = 9 − 3
- 1x = 6
- x = 6
- Check: LHS = RHS = 39 ✓
- Answer: x = 6
Worked example 3 (Challenge)
Solve: 3(9x − 14) = 15x − 54
- Expand: 27x − 42 = 15x − 54
- 12x = -12
- x = -1
- Answer: x = -1
Common mistakes and misconceptions
- Not changing sign when transposing
- Expanding brackets with a negative incorrectly
Practice questions
- (Basic) Solve: 3x − 14 = 5x − 28
- (Basic) Solve: 3x − 5 = 7x − 17
- (Standard) Solve: 3x − 4 = 7x + 16
- (Standard) Solve: 9x − 15 = 5x + 1
- (Challenge) Solve: 3(8x − 5) = 18x + 51
- (Challenge) Solve: 4(3x − 9) = 8x − 28
Answer key with full working
- Q1: 3x − 5x = -28 + 14 → -2x = -14 → x = 7 → Check: LHS = RHS = 7 ✓ → Answer: x = 7
- Q2: 3x − 7x = -17 + 5 → -4x = -12 → x = 3 → Check: LHS = RHS = 4 ✓ → Answer: x = 3
- Q3: 3x − 7x = 16 + 4 → -4x = 20 → x = -5 → Check: LHS = RHS = -19 ✓ → Answer: x = -5
- Q4: 9x − 5x = 1 + 15 → 4x = 16 → x = 4 → Check: LHS = RHS = 21 ✓ → Answer: x = 4
- Q5: Expand: 24x − 15 = 18x + 51 → 6x = 66 → x = 11 → Answer: x = 11
- Q6: Expand: 12x − 36 = 8x − 28 → 4x = 8 → x = 2 → Answer: x = 2
Syllabus note
This skill is listed under "Linear Equations in One Variable" for Class 8 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 linear equations with the variable on both sides in?
"Linear Equations in One Variable", Class 8 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.