A Budget That Shrinks
Part of the Inequalities & Absolute Value section of Coddy's Math 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
A phone has 80 percent battery and loses 6 percent an hour. For how many hours will it still have at least 20 percent?
The hours are x. Solve 80 - 6x >= 20 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