A Chain with a Flip

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

-3 < 2 - x <= 4: subtract 2 from all parts, then divide all parts by -1, flipping both signs.

-5 < -x <= 2

5 > x >= -2

Read small to large: -2 <= x < 5. The chain rule and the flip rule, together.

Nothing new, and that is the point of a final chapter: every inequality you will meet is a combination of the handful of moves in this section, and the only trap is the flip.

Challenge

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