Solving linear inequalities: Class 11 practice
Solve like an equation, but reverse the inequality sign when multiplying or dividing by a negative number. Read the method, follow the three worked examples, then try the six questions.
What you should know first
- Linear equations
The idea behind solving linear inequalities
Solve like an equation, but reverse the inequality sign when multiplying or dividing by a negative number. Write the answer as an inequality or interval.
Step-by-step method
- Collect x terms on one side.
- Divide by the coefficient; flip the sign if it is negative.
- Write the solution set.
Worked example 1 (Basic)
Solve 6x + 17 ≤ -13.
- 6x ≤ -30
- x ≤ -5
- Answer: x ≤ -5
Worked example 2 (Standard)
Solve -4x + 18 ≤ 10.
- -4x ≤ -8
- Divide by -4 and flip: x ≥ 2
- Answer: x ≥ 2
Worked example 3 (Challenge)
Solve -31 ≤ 5x − 16 ≤ -1.
- Subtract -16 from all parts: -15 ≤ 5x ≤ 15
- Divide by 5
- Answer: -3 ≤ x ≤ 3 ([-3, 3])
Common mistakes and misconceptions
- Not flipping the sign for a negative divisor
- Using brackets wrongly in interval notation
Practice questions
- (Basic) Solve 2x − 20 > -16.
- (Basic) Solve 2x − 3 ≤ -7.
- (Standard) Solve -3x + 20 < 35.
- (Standard) Solve -5x − 10 < -35.
- (Challenge) Solve 3 ≤ 2x + 3 ≤ 11.
- (Challenge) Solve -14 ≤ 4x + 10 ≤ 26.
Answer key with full working
- Q1: 2x > 4 → x > 2 → Answer: x > 2
- Q2: 2x ≤ -4 → x ≤ -2 → Answer: x ≤ -2
- Q3: -3x < 15 → Divide by -3 and flip: x > -5 → Answer: x > -5
- Q4: -5x < -25 → Divide by -5 and flip: x > 5 → Answer: x > 5
- Q5: Subtract 3 from all parts: 0 ≤ 2x ≤ 8 → Divide by 2 → Answer: 0 ≤ x ≤ 4 ([0, 4])
- Q6: Subtract 10 from all parts: -24 ≤ 4x ≤ 16 → Divide by 4 → Answer: -6 ≤ x ≤ 4 ([-6, 4])
Syllabus note
This skill is listed under "Linear Inequalities" for Class 11 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 linear inequalities in?
"Linear Inequalities", Class 11 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.