Equivalence Transformation Math Example 4

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

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

1
If we multiply $x = 5$ by 0: $0 \cdot x = 0 \cdot 5$ , giving $0 = 0$ .
2
$0 = 0$ is true for ALL $x$ , so we've lost information about the original solution.

Answer

Multiplying by 0 makes every value a solution, destroying the original solution set.

Multiplying by zero is not an equivalence transformation because it collapses all equations to

0 = 0

, which tells us nothing about

x

About Equivalence Transformation

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

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

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

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