Brackets and a Flip
Part of the Inequalities & Absolute Value section of Coddy's Math journey. Lesson 60 of 64.
The longer inequalities are the short ones in sequence. 3(x - 2) >= 5x - 4: distribute, gather, and the coefficient that is left is negative, so the last division flips.
3x - 6 >= 5x - 4
-2x - 6 >= -4
-2x >= 2
x <= -1
Or gather toward the 5x instead and end with -1 >= x, read as x <= -1. Either way: one flip, or one swap at the end, never both.
Before you start, count the layers: a bracket, x-terms on both sides, numbers on both sides. Then it is four moves, and the only question at each is whether it flips the sign.
Challenge
Solve the inequality 2(x + 1) - 3x < x + 10 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