Between, Shifted

Part of the Inequalities & Absolute Value section of Coddy's Algebra journey. Lesson 49 of 64.

The inequality |x - 1| <= 2 asks for the numbers within two steps of 1. Split it into a chain, then add 1 to all three parts:

-2 <= x - 1 <= 2

-1 <= x <= 3

$|x - 1| ≤ 2: within two steps of 1, that is from -1 to 3$

|x - 1| ≤ 2: within two steps of 1, that is from -1 to 3

Two moves you already know solve it: the split from the last lesson, then the chain work from chapter 7. The answer is a segment centred on 1, two steps to each side. The distance from x to 1 is at most 2, so x lies between -1 and 3.

Challenge

Medium

Solve the inequality |x + 2| < 5 for x.

Try it yourself

|x + 2| < 5

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: BetweenBetween, ShiftedGreater 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