A Wide Absolute Value
Part of the Inequalities & Absolute Value section of Coddy's Math journey. Lesson 62 of 64.
|3x - 6| <= 9: a "less than", so a chain; then two moves on all parts.
-9 <= 3x - 6 <= 9
-3 <= 3x <= 15
-1 <= x <= 5
Within 9 of zero for 3x - 6 turns into within 3 of 2 for x, which is the segment from -1 to 5.
Isolate the bars (already done here), split by the sign into a chain or an "or", then the ordinary rules on each piece. The split is the decision; the rest is routine.
Challenge
Solve the inequality |2x + 2| < 8 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 Equations12Final Challenges
Brackets and a FlipA Chain with a FlipA Wide Absolute ValueOutside, with a FractionThe Picture at the End