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Two Limits

Part of the Inequalities & Absolute Value section of Coddy's Algebra journey. Lesson 58 of 64.

Some conditions have a lower limit and an upper limit at the same time. A room must stay between 10 and 30 degrees. A heater starts at 4 degrees and adds 2 degrees for each notch. Which notches are allowed? Call the notch x. The temperature at notch x is 2x + 4. "Between 10 and 30" gives a chain inequality:

10 <= 2x + 4 <= 30

6 <= 2x <= 26

3 <= x <= 13

Notches 3 through 13 are allowed. Two limits in the words give a chain in the algebra. You solve the chain by doing each step on all three parts.

"Between a and b" includes the ends when the story says "from a to b" or "at least a and at most b". It leaves the ends out when the story says "strictly between". Read the phrase and choose ≤ or <. Then solve the chain the same way as before.

Challenge

Medium

A recipe needs the oven on for between 15 and 36 minutes, ends included. 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

15 <= 3x + 6 <= 36

Solve for x

Test yourself

This 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 Signs A Picture on a Line Closed or Open Reading It Backwards Recap: What an Inequality Is

4Two-Step Inequalities

Two Steps Subtract, Then Flip With a Fraction A Bracket on the Way Recap: Two-Step Inequalities

7Between Two Numbers

Two Conditions at Once Solving a Chain Two Moves on All Parts When the Chain Flips Chains with Fractions Recap: Between Two Numbers

10Absolute Value Inequalities

Less Than: Between Between, Shifted Greater Than: Outside Outside, Shifted Isolate, Then Split Always or Never Recap: Absolute Inequalities

2Adding and Subtracting

Add to Both Sides Subtract from Both Sides Negatives in the Mix Solve, Then Draw Recap: Adding and Subtracting

5Variables on Both Sides

x on Both Sides Gather Toward the Larger Brackets First Always True, Never True Recap: Variables on Both Sides

8One or the Other

Either Works Solving Each Part And versus Or Recap: One or the Other

11From Words to Inequalities

At Least, At Most More Than A Budget That ShrinksTwo LimitsRecap: From Words