Between, Shifted

Part of the Inequalities & Absolute Value section of Coddy's Algebra journey. Lesson 46 of 61.

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

$-2 \le x-1 \le 2$

$-1 \le x \le 3$

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

|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 $\left|x+2\right| < 5$ for $x$ .

Try it yourself

\left|x+2\right| < 5

Get $x$ alone on one side

All lessons in Inequalities & Absolute Value

1What an Inequality Is

The Four Signs A Picture on a Line 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 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