With a Fraction

Part of the Inequalities & Absolute Value section of Coddy's Math journey. Lesson 19 of 64.

x/2 - 1 > 3: add 1 to both sides, then multiply by 2. Both are sign-safe.

x/2 > 4

x > 8

Or clear the fraction first by multiplying everything by 2: x - 2 > 6, then add 2. Same answer, same number of steps.

Clearing the fraction first is often the calmer route when the fraction is a whole side, as in (x + 1)/3 <= 2: multiply both sides by 3 to get x + 1 <= 6, then subtract 1: x <= 5. Either order works; pick the one with the least arithmetic.

Challenge

Solve the inequality x/3 + 2 <= 4 for x.

Try it yourself

x/3 + 2 <= 4

Solve for x

Test yourself

This lesson includes a short quiz. Start the lesson to answer it and track your progress.

All lessons in Inequalities & Absolute Value

1What an Inequality Is

The Four Signs A Picture on a Line Closed or Open Reading It Backwards Recap: What an Inequality Is

4Two-Step Inequalities

Two Steps Subtract, Then FlipWith a FractionA Bracket on the Way Recap: Two-Step Inequalities

7Between Two Numbers

Two Conditions at Once Solving a Chain Two Moves on All Parts When the Chain Flips Chains with Fractions Recap: Between Two Numbers

10Absolute Value Inequalities

Less Than: Between Between, Shifted Greater Than: Outside Outside, Shifted Isolate, Then Split Always or Never Recap: Absolute Inequalities

2Adding and Subtracting

Add to Both Sides Subtract from Both Sides Negatives in the Mix Solve, Then Draw Recap: Adding and Subtracting

5Variables on Both Sides

x on Both Sides Gather Toward the Larger Brackets First Always True, Never True Recap: Variables on Both Sides

8One or the Other

Either Works Solving Each Part And versus Or Recap: One or the Other

11From Words to Inequalities

At Least, At Most More Than A Budget That Shrinks Two Limits Recap: From Words