Equivalence Transformation Math Example 3

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

Example 3

easy
What equivalence transformation converts 3x=153x = 15 to x=5x = 5?

Solution

  1. 1
    Divide both sides by 3: 3x3=153\frac{3x}{3} = \frac{15}{3}, giving x=5x = 5.
  2. 2
    This preserves the solution set because we divided by a nonzero number.

Answer

Divide both sides by 3.
Dividing by a nonzero constant is an equivalence transformation that preserves all solutions.

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 1 easy

Starting from [formula], apply an equivalence transformation to solve.

Example 2 medium

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

Example 4 medium

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

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