Absolute Value Inequalities Math Example 3

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

Example 3

easy
Solve ∣x−4∣≤2|x - 4| \leq 2.

Solution

  1. 1
    −2≤x−4≤2-2 \leq x - 4 \leq 2. Add 4: 2≤x≤62 \leq x \leq 6.
  2. 2
    Interval: [2,6][2, 6].

Answer

2≤x≤62 \leq x \leq 6
This means xx is within 2 units of 4 on the number line.

About Absolute Value Inequalities

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

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More Absolute Value Inequalities Examples

Example 1 easy

Solve [formula].

Example 2 medium

Solve [formula].

Example 4 hard

Solve [formula].

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