Absolute Value Equations Math Example 1

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

Example 1

easy
Solve ∣x−3∣=7|x - 3| = 7.

Solution

  1. 1
    ∣A∣=k|A| = k means A=kA = k or A=−kA = -k.
  2. 2
    Case 1: x−3=7⇒x=10x - 3 = 7 \Rightarrow x = 10.
  3. 3
    Case 2: x−3=−7⇒x=−4x - 3 = -7 \Rightarrow x = -4.
  4. 4
    Check: ∣10−3∣=7|10-3| = 7 ✓ and ∣−4−3∣=7|-4-3| = 7 ✓

Answer

x=10 or x=−4x = 10 \text{ or } x = -4
Absolute value equations always split into two cases because the expression inside can be either positive or negative. Both cases must be checked.

About Absolute Value Equations

Absolute value equations solve for values whose distance from zero or another number matches a target amount.

Learn more about Absolute Value Equations →

More Absolute Value Equations Examples

Example 2 medium

Solve [formula].

Example 3 easy

Solve [formula].

Example 4 medium

Solve [formula].

← All Absolute Value Equations Examples Absolute Value Equations Concept