Subtract from Both Sides

Part of the Inequalities & Absolute Value section of Coddy's Math journey. Lesson 7 of 64.

Subtracting the same amount from both sides is just as safe. x + 5 <= 2: subtract 5 from both sides.

x + 5 - 5 <= 2 - 5

x <= -3

The answer dips below zero, and that is fine: every number up to and including -3 works. -3 + 5 = 2 and 2 is indeed less than or equal to 2.

Adding and subtracting are the two moves that never touch the sign. Whatever you add to one side, add to the other; whatever you subtract from one side, subtract from the other; the sign stays as it was.

Challenge

Solve the inequality x + 9 <= 4 for x.

Try it yourself

x + 9 <= 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 Flip With a Fraction A 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 SidesSubtract from Both SidesNegatives 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