Contradiction Math Example 4

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

Example 4

medium
Solve ∣x∣=−5|x| = -5.

Solution

  1. 1
    Absolute value is always ≥0\geq 0.
  2. 2
    ∣x∣=−5|x| = -5 is impossible. Contradiction — no solution.

Answer

No solution.
Since absolute value is non-negative by definition, setting it equal to a negative number produces a contradiction. No real number xx satisfies ∣x∣=−5|x| = -5.

About Contradiction

A mathematical statement that is always false — no values of the variables can ever make it true.

Learn more about Contradiction →

More Contradiction Examples

Example 1 easy

Show that [formula] is a contradiction.

Example 2 medium

Solve [formula].

Example 3 easy

Is [formula] a contradiction or an identity?

← All Contradiction Examples Contradiction Concept

Related Concepts

EquationsConsistency