Negatives in the Mix

Part of the Inequalities & Absolute Value section of Coddy's Math journey. Lesson 8 of 64.

Negative numbers on either side change nothing about the method. x - 7 < -2: add 7 to both sides.

x < -2 + 7

x < 5

Adding 7 to -2 is the integer arithmetic from before: start at -2 and go up 7 to reach 5. Then the picture: an open dot at 5, shaded to the left.

One habit worth keeping: after solving, test one number from your range in the original inequality. For x < 5, try 0: 0 - 7 = -7, and -7 is less than -2. Good. A test number costs ten seconds and catches a sign slip every time.

Challenge

Solve the inequality x - 3 < -8 for x.

Try it yourself

x - 3 < -8

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 Sides Subtract from Both SidesNegatives in the MixSolve, 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