Algebra 1 / Unit 3: Solving Inequalities
3.4 Absolute Value Inequalities
Notes
- $|x| < a$ means $x$ is within $a$ of 0: $-a < x < a$ (an "and" inequality).
- $|x| > a$ means $x$ is more than $a$ away from 0: $x < -a$ or $x > a$ (an "or" inequality).
- Isolate the absolute value first. Example: $|x - 5| \le 2 \Rightarrow -2 \le x - 5 \le 2 \Rightarrow 3 \le x \le 7$.
Practice
Solve $|x| < 6$.
Within 6 units of zero.
Solve $|x + 1| \ge 4$.
$x + 1 \le -4$ or $x + 1 \ge 4$.
A machine part must be 50 mm long, give or take 0.2 mm. Which inequality describes acceptable lengths $L$?
The distance from 50 must be at most 0.2.
Ready for more? Take the Unit 3 test.