Absolute Value Inequalities Math Example 1

Follow the full solution, then compare it with the other examples linked below.

Example 1

easy
Solve ∣x∣<5|x| < 5.

Solution

  1. 1
    ∣x∣<5|x| < 5 means xx is less than 5 units from zero.
  2. 2
    This translates to −5<x<5-5 < x < 5.
  3. 3
    Interval notation: (−5,5)(-5, 5).

Answer

−5<x<5-5 < x < 5
For ∣A∣<k|A| < k (less than), the solution is a compound inequality −k<A<k-k < A < k. Think of it as 'between.'

About Absolute Value Inequalities

Absolute value inequalities describe values within or outside a fixed distance from a center.

Learn more about Absolute Value Inequalities →

More Absolute Value Inequalities Examples

Example 2 medium

Solve [formula].

Example 3 easy

Solve [formula].

Example 4 hard

Solve [formula].

← All Absolute Value Inequalities Examples Absolute Value Inequalities Concept