A Budget That Shrinks
Part of the Inequalities & Absolute Value section of Coddy's Algebra journey. Lesson 57 of 64.
You have 50 and spend 4 a day. For how many days will you still have at least 10? After x days you have 50 - 4x, and "at least 10" is ≥:
50 - 4x >= 10
-4x >= -40
x <= 10
Dividing by -4 flips the sign, and the answer reads: for up to 10 days. That matches sense: more days means less money, so the condition is a ceiling on days, not a floor.
A quantity that decreases carries a negative coefficient, and a negative coefficient brings the flip. When an answer comes out the "wrong way round" for the story, that is usually the flip that was missed.
Challenge
MediumA phone starts the day at 80% battery and loses 5% every hour. It must stay at 20% or more: 80 - 5x >= 20, where x is the number of hours. Solve 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 Solutions