Integrated Math 1 / Unit 2: Equations and Inequalities
2.4 Compound Inequalities
Notes
A compound inequality joins two inequalities. "And" means both must be true; "or" means at least one is true.
- "And" solutions are written as one statement, like $2 < x \leq 7$ (an overlap).
- "Or" solutions are separate pieces, like $x < -1$ or $x \geq 4$.
- Do the same step to all three parts of $a < \text{expression} < b$.
- Example: $-2 < 2x + 4 \leq 10 \Rightarrow -6 < 2x \leq 6 \Rightarrow -3 < x \leq 3$.
Practice
Solve $-2 < 2x + 4 \leq 10$.
Subtract 4 from all parts, then divide all parts by 2.
Which number is a solution of "$x < -1$ or $x \geq 4$"?
4 satisfies $x \geq 4$. The numbers 0, 2 and 3 satisfy neither part.
Which describes the solutions of "$3x > 6$ and $x < 5$"?
$3x > 6$ gives $x > 2$. Both conditions together give $2 < x < 5$.
Ready for more? Take the Unit 2 test.