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Less Than: Between

Part of the Inequalities & Absolute Value section of Coddy's Math journey. Lesson 48 of 64.

|x| < 3 asks for the numbers less than three steps from zero: everything between -3 and 3. As a chain:

-3 < x < 3

$|x| < 3: the numbers within three steps of zero$

|x| < 3: the numbers within three steps of zero

So an absolute value that is less than a number splits into a chain: |u| < c becomes -c < u < c. With ≤ the ends are included: |x| <= 3 is -3 <= x <= 3. Think "close to zero": a small absolute value means the number is near zero, on either side.

Challenge

Solve the inequality |x| <= 4 for x.

Try it yourself

|x| <= 4

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, 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