Study Guide: Section 7-6
Solving Open Sentences with Absolute Value
An open sentence involving absolute value can be solved by rewriting it as an equivalent compound inequality:
- For all real numbers a and b, with b > 0, the expression |a| < b is equivalent to the compound sentence −b < a < b (an and sentence, representing the intersection of two conditions).
- For all real numbers a and b, with b > 0, the expression |a| > b is equivalent to the compound sentence a < −b or a > b (an or sentence, representing the union of two conditions).
Remember: On a number line, |x| represents the distance between x and 0. Distance is never negative.
Examples 1 & 2: Absolute Value Inequalities
Example 3: Multi-Step Absolute Value Solutions
