Mastering One Step Inequalities

Introduction

Welcome to the fifth and final lesson of Solving One-Step Inequalities! Over the previous four lessons, you built up a toolkit of individual techniques: adding and subtracting, multiplying and dividing by positives, flipping the sign when negatives are involved, and rewriting results when the variable ends up on the right. Each time, you knew in advance which technique to use because the lesson told you. Starting now, the training wheels come off. This lesson shows you how to look at any one-step inequality, figure out what it needs, and solve it correctly — all on your own.

Three Cases, One Decision

Every one-step inequality you will encounter falls into one of three categories. The category depends entirely on what is being done to the variable, and it determines both the inverse operation you need and whether the inequality symbol changes direction.

CaseWhat is happening to xxInverse operationFlip the sign?
AdditiveA number is added to or subtracted from xxSubtract or add that numberNo
Positive scalingxx is multiplied or divided by a positive numberDivide or multiply by that numberNo
Negative scalingxx is multiplied or divided by a negative numberDivide or multiply by that numberYes

Only one of the three cases — negative scaling — requires reversing the inequality symbol. Two out of three leave it alone. Keeping that ratio in mind helps you resist the urge to flip when no flip is warranted. The rest of this lesson turns this table into a quick, repeatable process you can apply to any problem.

Step 1: Identify the Operation on the Variable

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