Activities

1. Write an inequality to represent a number is less than 8

2. Write an inequality to represent a number is greater than or equal to 22

3. Represent x ≤ 6 on a number line

    

4. Show x > -5 on a number line

   

5. Wendy spends at least 45 minutes each night doing her homework. Write an inequality to represent this situation and explain your answer.

6. Todd is swimming laps in a pool.  He wants to swim 5 laps in less than 12 minutes.  Write an inequality to represent this situation. 

7. While you were on vacation the temperature was greater than 75° F each day.  Write an inequality to represent this situation and show it on a number line.

8. The maximum number of people that a movie theater can hold is 175 people.  Write an inequality to represent the situation.  Explain what type of numbers can be used for the variable in the inequality.   

9. Selena graphed the following inequality shown below:

       Selena said that this represents the inequality n > -3.  Henry said that she was incorrect and that she actually graphed n ≥ -3.  

       Identify who is correct and explain why.

Answer Key/Rubric

1. n < 8

2. n ≥ 22

3. 

5. t ≥ 45

        Reasons to use this inequality may include, but are not limited to:

• t can represent time spent doing homework
• The wording “at least” means that that the time she spends working is 45 minutes or more
• The symbol ≥ is greater than or equal to

6. 5x < 12

        Reasons to use this inequality might be, but are not limited to

• 5x represents the 5 laps that are being swam
• 12 represents the total time to swim the laps
• Less than means that they do not want to get up to 12 minutes
• The symbol < is less than

7. t > 75

8. p ≤ 175

The numbers that can satisfy this inequality are:

• Any positive whole number between 0-175
• Anything less than 175, also including 175 because it can hold 175 people, no more
• Numbers below zero won’t make sense in this situation as we are referring the number of people

9. Henry is correct.

Reasons might include, but are not limited to:

• Selena graphed using a closed circle on her number line
• A closed circle indicates that the value the circle is on is included as part of the inequality
• Selena’s inequality used a > symbol which only means numbers greater than -3, not including -3
• Henry’s inequality used a ≥ symbol which means that all values greater than -3, including the -3 are part of the inequality