Chains with Fractions
Part of the Inequalities & Absolute Value section of Coddy's Algebra journey. Lesson 35 of 64.
In 0 <= x/2 < 3, the middle is half of x. To undo a division, multiply. Multiply all three parts by 2:
0 <= x < 6
Half of x is between 0 and 3, so x is between 0 and 6. Multiplying by a positive number keeps both signs. If the middle were -x/2, you would multiply by -2, and both signs would flip.
A fraction in the middle is undone by multiplying all parts by its denominator. Before you multiply, ask one question: is the multiplier positive or negative? A positive multiplier keeps the signs, and a negative multiplier flips both. The size of the multiplier does not matter.
Challenge
MediumSolve the compound inequality -2 < x/3 <= 1 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