Inequalities in One Variable
10-2Solving Inequalities
Overview
Use the same moves as for equations, BUT reverse the inequality when multiplying or dividing by a negative.
Key ideas
- Add/subtract: inequality stays the same.
- Multiply/divide by positive: stays the same.
- Multiply/divide by negative: FLIP the sign.
Worked examples
Example 1
Problem. Solve x + 5 < 9.
Solution. x < 4
Example 2
Problem. Solve −2x ≥ 8.
Solution. Divide by −2 and flip: x ≤ −4.
Practice
Try each one. Click Show answer when ready.
- 1.
Solve 3x > 12.
- 2.
Solve −x ≤ 5.
- 3.
Solve 2x + 1 < 7.
Challenge problems
A little tougher — great for test prep. Click Show answer when ready.
- 1.
Solve: 3(2x − 1) < 5x + 4.
- 2.
Solve: −4(x + 2) ≥ 3x − 6.