A Budget That Shrinks
Part of the Inequalities & Absolute Value section of Coddy's Algebra journey. Lesson 57 of 64.
You have 50 and you spend 4 a day. For how many days will you still have at least 10? Call the number of days x. After x days you have 50 - 4x. "At least 10" means 10 or more, so the sign is ≥:
50 - 4x >= 10
-4x >= -40
x <= 10
Dividing by -4 flips the sign. The answer is that you can go on for up to 10 days. Check the answer against the story. More days means less money, so the condition sets an upper limit on the days, not a lower limit.
A quantity that goes down has a negative coefficient on x. When you divide by that negative coefficient to get x alone, reverse the inequality sign. Then check that the range you found fits the story.
Challenge
MediumA phone starts the day at 80% battery and loses 5% every hour. It must stay at 20% or more. With x as the number of hours, the condition is 80 - 5x >= 20. 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