Inverse Operations

Pre-Algebra · Axiom Academy

Solve equations by using the operations that undo each other — keeping both sides perfectly balanced. 1. What Are Inverse Operations? Think of a short journey: walk 5 steps forward, then 5 steps back, and you're exactly where you began. The two moves cancel. Watch a number make the round trip — once with , once with — and land right back on itself. Addition and subtraction are inverse operations. If you add a number, you can get back to where you started by subtracting that same number. On a number line this is a walk out and a walk back. 3. Multiplication and Division Multiplication and division are inverse operations. If you multiply by a number, you can get back to the original by dividing by that same number — as long as it isn't zero. Watch one group grow into several, then collapse back to one. 4. The Balance Scale Principle An equation is like a balanced scale — both sides carry equal weight. The instant you change just one side, the scale tips. To keep it level, whatever you do to one side you must do to the other. 5. Solving with Addition / Subtraction To solve x + 5 = 12 we need x alone. Since 5 is being added to x , we apply its inverse — subtract 5 — from both sides. The +5 and -5 cancel on the left, isolating x . 6. Solving with Multiplication / Division To solve 3x = 15 we need x alone. Since x is being multiplied by 3 , we apply its inverse — divide by 3 — on both sides. The and cancel on the left, isolating x .

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