The Universal Calculation Engine
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The Universal Calculation Engine

Why multiplying both sides keeps truth

Part of: Solving Equations

A useful rule about equations: what stays true when the numbers change.

The rule

The rule is the part that still works when you try new examples. Solving Equations puts it in context with practice.

Why it works

Example: multiplying both sides of a true equation by the same nonzero number gives another true equation, because every term was scaled by the same factor.

Small numbers

Try 2 + 3 = 5. Multiply both sides by 4: 8 + 12 = 20. Still true. That is the same idea as “do the same thing to both sides” when you solve.

Test it

The rule
A quick test

Try values

Core lesson

Go deeper: Solving Equations. Use the calculators below with your own loan or bill numbers, not only the examples on this page.

Use the calculator

FAQ

Where is the main lesson?

Solving Equations has the full topic, examples, and practice links.

Which calculator first?

After your setup is on paper, open Linear & quadratic equation for a quick numeric pass.