The Equation |x| = 3
Part of the Inequalities & Absolute Value section of Coddy's Math journey. Lesson 42 of 64.
|x| = 3 asks: which numbers are three steps from zero? Two of them, 3 and -3. An absolute value equation usually has two solutions, one on each side of zero:
x = 3
or
x = -3
The single line |x| = 3 splits into two ordinary equations, and both answers count. Check each: |3| = 3 and |-3| = 3.
Splitting is the one new move of this chapter: |u| = c becomes u = c or u = -c. Everything after the split is the equation solving you already know, done once for each case.
Challenge
Solve the equation |x| = 5 for x.
Try it yourself
Solve for x
Test yourselfThis 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 SignsA Picture on a LineClosed or OpenReading It BackwardsRecap: What an Inequality Is4Two-Step Inequalities
Two StepsSubtract, Then FlipWith a FractionA Bracket on the WayRecap: Two-Step Inequalities2Adding and Subtracting
Add to Both SidesSubtract from Both SidesNegatives in the MixSolve, Then DrawRecap: Adding and Subtracting5Variables on Both Sides
x on Both SidesGather Toward the LargerBrackets FirstAlways True, Never TrueRecap: Variables on Both Sides11From Words to Inequalities
At Least, At MostMore ThanA Budget That ShrinksTwo LimitsRecap: From Words3Multiplying and Dividing
Divide by a PositiveMultiply by a PositiveThe FlipDividing by a NegativeNegative FractionsRecap: Multiply and Divide6Graphing Solutions
From Inequality to PictureIs the Endpoint In?A Flip on the LineRecap: Graphing Solutions9Absolute Value Equations
Distance from ZeroThe Equation |x| = 3Distance from a PointIsolate the Bars FirstA Coefficient InsideNo Solution, One SolutionRecap: Absolute Equations