A Chain with a Flip

Part of the Inequalities & Absolute Value section of Coddy's Algebra journey. Lesson 61 of 64.

Take the chain -3 < 2 - x <= 4. Subtract 2 from all three parts. Then divide all three parts by -1, which flips both signs.

-5 < -x <= 2

5 > x >= -2

Read the result from small to large: -2 <= x < 5. This uses the chain rule and the flip rule together.

These exercises combine the steps from earlier in this section. Do each step on every part of the chain. When you multiply or divide by a negative number, reverse both inequality signs.

Challenge

Hard

Solve the compound inequality -4 <= 1 - x < 2 for x.

Try it yourself

-4 <= 1 - x < 2

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 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

3Multiplying and Dividing

Divide by a Positive Multiply by a Positive The Flip Dividing by a Negative Negative Fractions Recap: Multiply and Divide

6Graphing Solutions

From Inequality to Picture Is the Endpoint In?A Flip on the Line Recap: Graphing Solutions

9Absolute Value Equations

Distance from Zero The Equation |x| = 3 Distance from a Point Isolate the Bars First A Coefficient Inside No Solution, One Solution Recap: Absolute Equations

12Final Challenges

Brackets and a FlipA Chain with a FlipA Wide Absolute Value Outside, with a Fraction The Picture at the End