Combining Open Sentences
10-5Absolute Value in Open Sentences
Overview
|x| = a → x = a or x = −a. |x| < a → −a < x < a. |x| > a → x < −a or x > a (for a > 0).
Key ideas
- Equation with |…|: two cases.
- ‘Less than’ becomes a compound AND.
- ‘Greater than’ becomes a compound OR.
Worked examples
Example 1
Problem. Solve |x| = 5.
Solution. x = 5 or x = −5.
Example 2
Problem. Solve |x − 1| < 3.
Solution. −3 < x − 1 < 3 → −2 < x < 4.
Example 3
Problem. Solve |x + 2| > 4.
Solution. x + 2 < −4 or x + 2 > 4 → x < −6 or x > 2.
Practice
Try each one. Click Show answer when ready.
- 1.
Solve |x| = 7.
- 2.
Solve |x − 2| ≤ 3.
- 3.
Solve |x + 1| > 2.
Challenge problems
A little tougher — great for test prep. Click Show answer when ready.
- 1.
Solve: |2x − 3| = 7.
- 2.
Solve: |x + 4| = |2x − 1|.