Math
Solving inequalities.
Definition
The process of finding all values of a variable that make an inequality true. The steps are similar to solving equations, but you must reverse the inequality sign when multiplying or dividing by a negative number.
How it works · 4 phases
Step by step.
- Simplify both sides of the inequality.
- Use inverse operations to isolate the variable.
- If you multiply or divide by a negative number, flip the inequality sign.
- Write the solution in interval notation or graph it on a number line.
Examples
Real-world.
- 1 −3x > 12 → x < −4 (dividing by −3 flips the sign)
- 2 2x + 5 ≤ 11 → 2x ≤ 6 → x ≤ 3
Key Fact
Flip the inequality sign when multiplying or dividing by a negative number.