MathAlgebraMedium frequency
SAT Math: Absolute Value Inequalities
20+ practice questions in Praczo
What you need to know
The concept, explained
- 1
Absolute value measures distance from zero. |x| < a means the distance is LESS than a, trapping the value between -a and a (-a < x < a).
- 2
|x| > a means the distance is MORE than a, pushing the value outside the bounds (x > a OR x < -a).
- 3
If setting up an absolute value inequality for a word problem involving a target value T and an allowed margin m, use |x - T| ≤ m.
Common mistakes
- ✗ Forgetting to flip the inequality sign when setting up the negative case (e.g., turning |x-2|>5 into x-2>5 and x-2>-5, instead of x-2<-5).
- ✗ Answering "All real numbers" for |x| > -5 when it's actually a valid statement (absolute value is always ≥ 0, which is always > -5).
Try a sample question
SAT-style practice
A machine fills bags with 500 grams of flour. The acceptable margin of error is 5 grams. Which inequality represents the acceptable weight w?
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