Outside, Shifted

Part of the Inequalities & Absolute Value section of Coddy's Math journey. Lesson 51 of 64.

|2x + 1| >= 5: split into the two cases, then solve each as a two-step inequality.

2x + 1 >= 5

2x >= 4

x >= 2

2x + 1 <= -5

2x <= -6

x <= -3

The solution is x <= -3 or x >= 2: two rays pointing away from each other.

Each case is solved with the ordinary rules, including the flip if a negative coefficient turns up. Keep both cases to the end, and keep the word "or" between the two answers.

Challenge

Solve the inequality |x - 3| > 1 for x.

Try it yourself

|x - 3| > 1

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: OutsideOutside, ShiftedIsolate, 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