A Coefficient Inside

Part of the Inequalities & Absolute Value section of Coddy's Math journey. Lesson 45 of 64.

|2x - 1| = 7: split first, then each case is a two-step equation.

2x - 1 = 7

2x = 8

x = 4

and

2x - 1 = -7

2x = -6

x = -3

Two cases, two little equations, two answers: x = 4 or x = -3. Check one: |2 × -3 - 1| = |-7| = 7. The only new habit is keeping both cases going to the end.

Challenge

Solve the equation |2x + 3| = 9 for x.

Try it yourself

|2x + 3| = 9

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 Point Isolate the Bars FirstA Coefficient InsideNo 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