Isolate the Bars First

Part of the Inequalities & Absolute Value section of Coddy's Algebra journey. Lesson 44 of 64.

In |x + 3| - 2 = 4, the absolute value is not alone on its side. Before you split, get the absolute value by itself. Add 2 to both sides:

|x + 3| = 6

Now split into two cases: x + 3 = 6 or x + 3 = -6. Subtract 3 in each case to get x = 3 or x = -9.

The -2 in |x + 3| - 2 = 4 sits outside the absolute value bars, so it is not part of either case. Add 2 to both sides first to get |x + 3| = 6. Then solve x + 3 = 6 and x + 3 = -6 separately.

Challenge

Medium

Solve |x - 5| + 2 = 8.

Try it yourself

|x - 5| + 2 = 8

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 PointIsolate the Bars FirstA Coefficient Inside No Solution, One Solution Recap: Absolute Equations

12Final Challenges

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