Two Moves on All Parts
Part of the Inequalities & Absolute Value section of Coddy's Math journey. Lesson 33 of 64.
-6 <= 2x - 2 < 4: the middle is a two-step expression, so two moves on all parts. Add 2 to all parts, then divide all parts by 2.
-4 <= 2x < 6
-2 <= x < 3
Both moves are sign-safe, so both signs keep their direction and the ≤ on the left stays a ≤.
The chain is the two-step routine done three times at once: undo the added number, then the coefficient, on the left end, the middle and the right end together.
Challenge
Solve 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