Example 1 · level 1
Solve for real x: 3x − 10 ≤ −31.
- x < −7
- x ≥ −7
- x ≤ 7
- x ≤ −7
Show solution
- Add 10 to both sides: 3x ≤ −21.
- Divide by 3: x ≤ −7.
Answer: x ≤ −7
CLASS 11 MATHS · LINEAR INEQUALITIES
Solve linear inequalities in one variable
Solve like an equation, but when you multiply or divide both sides by a negative number, reverse the inequality sign.
Loading practice…
Worked examples
Example 2 · level 2
Solve for real x: −3x − 6 > −9.
- x > 1
- x ≤ 1
- x < 1
- x < −1
Show solution
- Add 6 to both sides: −3x > −3.
- Divide by −3 (negative, so reverse the sign): x < 1.
Answer: x < 1
Example 3 · level 3
Solve for real x: 4x − 5 ≤ 2x − 15.
- x ≤ 5
- x ≥ −5
- x < −5
- x ≤ −5
Show solution
- Collect x terms on the left and numbers on the right: 2x ≤ −10.
- Divide by 2: x ≤ −5.
Answer: x ≤ −5