Lesson 14: Finding Solutions to Inequalities in Context

Finding Solutions to Inequalities in Context

Colder and Colder

5 min

Problem

It is currently 10 degrees outside. The temperature is dropping 4 degrees every hour.

Explain what the equation $10 - 4h=\text-2$ represents.
What value of $h$ makes the equation true?
Explain what the inequality $10 -4h < \text-2$ represents.
Does the solution to this inequality look like $h < \text{\_\_}$ or $h > \text{\_\_}$ ? Explain your reasoning.

Answer

Sample response: when the temperature is exactly -2 degrees
$h=3$
Sample response: When the temperature is colder than -2 degrees
$h > \text{\_\_}$ . Sample reasoning: The solution is $h > 3$ . Since the temperature is dropping, it will be colder than -2 degrees after 3 hours.

Sample Response

Sample response: when the temperature is exactly -2 degrees
$h=3$
Sample response: When the temperature is colder than -2 degrees
$h > \text{\_\_}$ . Sample reasoning: The solution is $h > 3$ . Since the temperature is dropping, it will be colder than -2 degrees after 3 hours.

Responding to Student Thinking

More Chancesmore_chances

Response: Students will have more opportunities to understand the mathematical ideas addressed here. There is no need to slow down or add additional work to the next lessons.

Standards

Addressing

7.EE.4.b·Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.
7.EE.B.4.b·Solve word problems leading to inequalities of the form $px + q > r$ or $px + q < r$, where $p$, $q$, and $r$ are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. \$