Two Moves on All Parts
Part of the Inequalities & Absolute Value section of Coddy's Algebra journey. Lesson 33 of 64.
In -6 <= 2x - 2 < 4, the middle is 2x - 2. It takes two steps to get x alone, and each step is done to all three parts. First add 2 to all three parts. Then divide all three parts by 2:
-4 <= 2x < 6
-2 <= x < 3
Adding a number does not change an inequality sign, and dividing by a positive number does not either. So both signs keep their direction, and the ≤ on the left stays a ≤.
Solving this chain is the same as solving a two-step inequality, done to three parts at the same time. First undo the added number, then undo the coefficient. Each step is done to the left end, the middle and the right end together.
Challenge
MediumSolve the compound inequality 1 <= 3x + 4 < 13 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 Inequalities7Between Two Numbers
Two Conditions at OnceSolving a ChainTwo Moves on All PartsWhen the Chain FlipsChains with FractionsRecap: Between Two Numbers2Adding 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 Solutions