Isolate the Bars First
Part of the Inequalities & Absolute Value section of Coddy's Math journey. Lesson 44 of 64.
|x + 3| - 2 = 4: the absolute value is not alone yet. Before splitting, get the bars by themselves: add 2 to both sides.
|x + 3| = 6
Now split: x + 3 = 6 or x + 3 = -6, so x = 3 or x = -9.
Splitting too early is the classic slip. |x + 3| - 2 = 4 does not mean x + 3 - 2 = 4 or its negative; the -2 is outside the bars and must be moved away first. The rule: isolate the absolute value, then split, then solve each case.
Challenge
Solve the equation |x - 2| + 1 = 6 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