College Algebra / Unit 3 Alg 172 worked example, 60 to 90 seconds
Solving an Absolute Value Inequality
The idea
Solving an absolute value inequality means isolating the absolute value, unpacking by the less-than or greater-than pattern, solving each piece, and writing the set in interval notation.
In practice
Solve |2x − 1| > 7. The absolute value already stands alone, and greater-than means rays: 2x − 1 > 7 or 2x − 1 < −7. Solve each: x > 4 or x < −3. Interval form: (−∞, −3) ∪ (4, ∞). Test all three regions: x = 5 gives |9| = 9 > 7, true; x = −4 gives |−9| = 9 > 7, true; x = 0 gives |−1| = 1 > 7, false — both rays admit, the middle rejects, exactly the greater-than shape. A less-than version would have produced one trapped interval instead of two rays.
Where people slip
Isolate the absolute value before unpacking; a coefficient outside the bars changes the k.
Your place on the trail
Every lesson rests on earlier ones and opens later ones. Tap any to jump.
Builds on
- Nothing. This is a starting point.
Unlocks
- Nothing yet depends on this.
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