Equivalence Transformation Math Example 1

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

Example 1

easy
Starting from x+5=12x + 5 = 12, apply an equivalence transformation to solve.

Solution

  1. 1
    Subtract 5 from both sides (an equivalence transformation): x=7x = 7.
  2. 2
    The transformation preserves the solution set: the solutions of x+5=12x + 5 = 12 and x=7x = 7 are identical.
  3. 3
    Any value satisfying one equation satisfies the other.

Answer

x=7x = 7
An equivalence transformation changes the form of an equation without changing its solution set. Adding, subtracting, multiplying, or dividing both sides by a nonzero constant are all equivalence transformations.

About Equivalence Transformation

Operations applied to both sides of an equation that transform its form while leaving its solution set completely unchanged.

Learn more about Equivalence Transformation →

More Equivalence Transformation Examples

Example 2 medium

Why is squaring both sides of an equation NOT always an equivalence transformation?

Example 3 easy

What equivalence transformation converts [formula] to [formula]?

Example 4 medium

Why must we NOT multiply both sides of an equation by 0?

← All Equivalence Transformation Examples Equivalence Transformation Concept