Combining Open Sentences
10-6Absolute Values of Products in Open Sentences
Overview
Solve absolute-value sentences whose argument is a product like |2x − 3|.
Key ideas
- Apply the same equation/inequality rules.
- Isolate the absolute value first if needed.
- Always check solutions.
Worked examples
Example 1
Problem. Solve |2x − 3| = 7.
Solution. 2x − 3 = 7 or = −7 → x = 5 or x = −2.
Example 2
Problem. Solve |3x + 1| < 5.
Solution. −5 < 3x + 1 < 5 → −2 < x < 4/3.
Practice
Try each one. Click Show answer when ready.
- 1.
Solve |2x + 1| = 9.
- 2.
Solve |3x − 6| ≤ 9.
- 3.
Solve |4x| > 8.
Challenge problems
A little tougher — great for test prep. Click Show answer when ready.
- 1.
Solve: |3x| + 2 = 11.
- 2.
Solve: 2|x − 1| − 3 = 5.