Solution Concept Math Example 2

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

Example 2

medium
Find all solutions of ∣x∣=5|x| = 5.

Solution

  1. 1
    The absolute value of xx equals 5 means xx is 5 units from zero.
  2. 2
    Two values satisfy this: x=5x = 5 and x=−5x = -5.
  3. 3
    Check: ∣5∣=5|5| = 5 ✓ and ∣−5∣=5|-5| = 5 ✓

Answer

x=5 or x=−5x = 5 \text{ or } x = -5
Some equations have multiple solutions. The absolute value equation ∣x∣=k|x| = k always has two solutions (when k>0k > 0) because both kk and −k-k are at the same distance from zero.

About Solution Concept

A specific value (or set of values) that makes an equation or inequality true when substituted in for the variable.

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More Solution Concept Examples

Example 1 easy

Is [formula] a solution of [formula]?

Example 3 easy

Which values are solutions of [formula]: [formula], [formula], [formula]?

Example 4 medium

Does the equation [formula] have any solutions?

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