Solving a Chain
Part of the Inequalities & Absolute Value section of Coddy's Algebra journey. Lesson 32 of 64.
To solve a chain, get x alone in the middle. In -3 < x + 1 < 5, the middle is x + 1. Whatever you do to the middle, you must do to all three parts, because the middle is compared with both ends. Subtract 1 from all three parts:
-3 - 1 < x + 1 - 1 < 5 - 1
-4 < x < 4
One step solves the chain. x is between -4 and 4.
A chain is two inequalities, -3 < x + 1 and x + 1 < 5. Subtracting 1 from all three parts is the same as subtracting 1 from both sides of each inequality. Writing them as one chain lets you do both steps in one line. When x is alone in the middle, the two ends give the answer.
Challenge
MediumSolve the compound inequality 2 < x + 4 < 9 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