Menu

English

Distance from a Point

Part of the Inequalities & Absolute Value section of Coddy's Algebra journey. Lesson 43 of 64.

The equation |x - 2| = 5 asks which numbers are five steps from 2. Split it into two cases, x - 2 = 5 or x - 2 = -5, then add 2 to both sides in each case:

x = 7

or

x = -3

$-3 and 7 are both five steps from 2$

-3 and 7 are both five steps from 2

The expression |x - a| is the distance between x and a. So |x - 2| = 5 says the distance between x and 2 is 5, and the two solutions are the two numbers five steps from 2. The algebra gives the same answer: split, solve each case, and the two answers are the same distance from 2, one on each side.

Challenge

Medium

Solve the equation |x - 1| = 4 for x.

Try it yourself

|x - 1| = 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: 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| = 3Distance from a PointIsolate the Bars First A 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