4.1 – Inequalities and Their Graphs!
Objectives:
1.
2.
1. What does this picture mean to you? (Explain in complete sentences)
2. If you were going to write an inequality for this picture, what symbol would you use? (  ,  , <, >,
 ) Why??
3. 60  65 is an inequality that represents one speed you could go on this road. You could go 60mph
and still be under the speed limit. Write two more inequalities like this.
4. Write one inequality for all of the possible speeds you could go on this road (legally).
5. What does this picture mean to you? (Explain)
6. Write an inequality that represents all of the possible wages you could earn at this shoe store.
7. In number 4 we wrote an inequality that says your speed on this road needs to be less than or
equal to 65. Are all of the numbers less than or equal to 65 reasonable in this situation? Why or
why not?
8. In number 6 we wrote an inequality that our income will be greater than or equal to $6.15/h. Are
all of the numbers greater than 6.15 reasonable in this situation? Why or why not?
9. Represent this inequality on a number line: s  65
10. All students at FRHS are at least 14 years old.
Write an inequality to represent this situation, and then graph it on a number line.
11. Rachel is a freshman at FRHS and is taking 7 classes. She and her parents have made a deal that
she will pay them $5 for every 'F' she has on her report card at the end of the semester. The end of
the semester is coming up and Rachel only has $2 in her bank account.
a. What if Rachel fails one class and gives her parents the $2 out of her bank account. How much
more money will she owe them?
b. How much more will she owe them if she fails two classes?
c. Three classes?
d. What is the most amount of money she could owe her parents at the end of the semester?
12. Which inequality best fits this problem? Why? (think about how you figured out the answers to
#11 to help you find the correct inequality!!)
a. 5x - 2 ≤ -33
b. 2 - 5x ≥ 33
c. 5x - 2 ≤ 33
d. -5x + 2 < -33
13. What does ‘x’ represent in the inequality you picked for #12?
14. Is 3.2 a solution to this inequality? (If you plug in 3.2 for x will you get a number that is less than
or equal to 33?)
15. Is 3.2 a reasonable solution for this problem? Why or why not?
16. Is each number a solution to the inequality 3x – 7 > 0?
a. 2
b. 5