Two Limits
Part of the Inequalities & Absolute Value section of Coddy's Math journey. Lesson 58 of 64.
Some conditions have a floor and a ceiling at once. A room must stay between 10 and 30 degrees; a heater raises the temperature by 2 degrees per notch from a base of 4. Which notches are allowed? The temperature at notch x is 2x + 4, and "between 10 and 30" is a chain:
10 <= 2x + 4 <= 30
6 <= 2x <= 26
3 <= x <= 13
Notches 3 through 13. Two limits in the words mean a chain in the algebra, and the chain is solved on all parts as usual.
"Between a and b" usually includes the ends when a story says "from a to b" or "at least a and at most b", and excludes them for "strictly between". Read the phrase, pick ≤ or <, and the rest is chapter 7.
Challenge
A recipe needs the oven between 15 and 36 minutes, ends included, and a dial setting of x gives a time of 3x + 6 minutes. Which settings work?
Solve 15 <= 3x + 6 <= 36 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