Contradiction Math Example 2

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

Example 2

medium
Solve 2(x+3)=2x+52(x + 3) = 2x + 5.

Solution

  1. 1
    Step 1: Distribute: 2x+6=2x+52x + 6 = 2x + 5.
  2. 2
    Step 2: Subtract 2x2x: 6=56 = 5.
  3. 3
    Step 3: Contradiction! No solution exists.

Answer

No solution (contradiction).
When the variable terms cancel and the remaining constants are unequal, the equation is a contradiction. This can also occur in systems when parallel lines or parallel planes have no intersection.

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 3 easy

Is [formula] a contradiction or an identity?

Example 4 medium

Solve [formula].

← All Contradiction Examples Contradiction Concept

Related Concepts

EquationsConsistency