At Least, At Most
Part of the Inequalities & Absolute Value section of Coddy's Math journey. Lesson 55 of 64.
Everyday phrases hide inequality signs. "At least 5" means 5 or more: x >= 5. "At most 5" means 5 or fewer: x <= 5. "More than 5" is strictly above: x > 5; "fewer than 5" or "less than 5" is strictly below: x < 5. "No more than" is "at most"; "no less than" is "at least".
A taxi charges 3 to start and 2 per kilometre. With at most 21 to spend, how far can you ride? The cost of x kilometres is 3 + 2x, and "at most 21" is ≤:
3 + 2x <= 21
2x <= 18
x <= 9
Up to 9 kilometres. The inequality is built exactly like the equations from words before; only the sign comes from the phrase.
Challenge
A pool charges 5 to enter and 3 per hour. With at most 26 to spend, how many hours can you stay?
The hours are x, and the cost is 5 + 3x. Solve 5 + 3x <= 26 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