Lesson 2
Solutions of Inequalities
Let’s think about the solutions to inequalities.
Problem 1
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Select all numbers that are solutions to the inequality \(k > 5\).
4
5
6
5.2
5.01
0.5
- Draw a number line to represent this inequality.
Problem 2
A sign on the road says: “Speed limit, 60 miles per hour.”
- Let \(s\) be the speed of a car. Write an inequality that matches the information on the sign.
- Draw a number line to represent the solutions to the inequality.
- Could 60 be a value of \(s\)? Explain your reasoning.
Problem 3
One day in Boston, MA, the high temperature was 60 degrees Fahrenheit, and the low temperature was 52 degrees.
- Write one or more inequalities to describe the temperatures \(T\) that are between the high and low temperature on that day.
- Show the possible temperatures on a number line.
Problem 4
Describe a rigid transformation that you could use to show the polygons are congruent.
![Triangles A B C and D E F.](https://cms-im.s3.amazonaws.com/xwXHVhqUtPxzYfCBDhhEymvc?response-content-disposition=inline%3B%20filename%3D%228-8.1.C.PP.Image.08.5b.png%22%3B%20filename%2A%3DUTF-8%27%278-8.1.C.PP.Image.08.5b.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240726%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240726T233453Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=c5cdbdb83e32e464116e9fbde8d37f93407519adf8ac93f915f00d36577ec5df)
Problem 5
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Jada is taller than Diego. Diego is 54 inches tall (4 feet, 6 inches). Write an inequality that compares Jada’s height in inches, \(j\), to Diego’s height.
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Jada is shorter than Elena. Elena is 5 feet tall. Write an inequality that compares Jada’s height in inches, \(j\), to Elena’s height.