Name:_________________________________________________Date:________________________Hour:___________

Unit 2: Inequalities Review KEY 1. Would it make more sense to say that the height restrictions at an amusement park are equations or inequalities? Explain your reasoning. The height restrictions would make more sense if they were described as inequalities because the restriction is not saying that your height must be equal to something (like 48 inches, for example). It is just setting a boundary and saying that your height must be that tall or taller. Your height must be greater than or equal to some number. That is an inequality. 2. The graph below represents the ages of people allowed inside the moon bounce. Write an inequality to represent the ages of people allowed to bounce. It starts at 2 (which is included because the circle is filled in) and goes to 7 (which is not included because the circle is not filled in). So the answer is: 2≤𝑥<7

3. Graph the inequality. −4 < 𝑥 ≤ 1 bigger than -4 and smaller than or equal to 1 < and >means open circle ≤ and ≥ means closed circle

1 -4 4. Graph the inequality. 𝑥 > 2 𝑎𝑛𝑑 𝑥 < −1 bigger than 2 and smaller than -1 < and >means open circle ≤ and ≥ means closed circle

-1

2

5. Solve the inequality and graph your solution on the graph below. 4𝑥 ≤ −16 4̅ 4̅ We need to get the x alone. We don’t flip the sign because the number we divided

𝑥 ≤ −4

by (4) is positive. Now graph. Closed circle because there is an equal and we want numbers smaller than -4. 6. Solve the inequality and graph your solution on the graph below. −4𝑥 + 2 ≤ 𝑥 − 3 Get the x alone by subtracting 2 on both sides. Get the x’s on one side by subtracting x from both sides. Get the x alone by dividing by -5. FLIP THAT SIGN, we divided by a negative. Now graph. Closed circle because there is an equal to and we want numbers bigger than 1.

Name:_________________________________________________Date:________________________Hour:___________ 7. Are there any mistakes in the work below? If the answer is no then you may just write “no”. If the answer is yes then you must identify the mistake(s) and explain what you would do differently and why. YES, there is a mistake on the last step. Whenever you multiply or divide by a negative you have to flip the inequality sign. They divided by a -5 to get the x alone, so they have to flip the inequality sign. The answer should be 𝑥 ≥

14 . 5

Solve the following compound inequalities and graph their solutions. 8.

−3 < −2𝑥 + 1 ≤ 9

Graph:

9.

Pretend like that’s on 2 instead of 3.

3𝑦 − 5 < −8 𝑜𝑟

2𝑦 − 1 > 5

Graph:

Write the statements as inequalities or equations, depending on what fits the context. 10. Amanda wears size 8 shoes. Write the mathematical statement of shoe sizes, s, that fit Amanda. 𝑠=8 We know it is an equation because Amanda can only wear size 8 shoes, there is only one shoe size that will work. 11. Curt can’t play outside unless it’s more than 70 degrees. Write the mathematical statement of temperatures, t, that make it so Curt can play outside. 𝑡 > 70 We know it is an inequality because Curt can play outside if its more than 70 degrees. He can play outside if its 70.0001 degrees or 80 degrees or 112 degrees or anything more than 70. 12. Brian will get in trouble if he hangs out with his friends after school more than 2 times a week. Write the mathematical statement of the number of days, d, Brian can hang out with friends in one week. 𝑑≤2 We know it is an inequality because Brian can hang out with his friends 2 or less times each week. He can hang out 2 times or 1 time or 0 times.

Name:_________________________________________________Date:________________________Hour:___________ 13. On Halloween the temperature in Vernal will vary from 30oF to 54oF. Write a compound inequality that represents the situation and then write three possible temperatures for the day. The temperature, 𝑡, will be 54 or less, and 30 or more. 30 ≤ 𝑡 ≤ 54 The temperature could be 50 or 35 or 52 0r 47, etc. etc. etc. 14. Solve the inequality and graph your solution on the graph below. |𝑥 − 2| > 1 To solve absolute value inequalities, we re-write the equation as two equations, without the absolute value sign, and change the way the inequality is facing and the sign on the answer for the second equation. Then we solve the inequalities like normal. 𝑥 − 2 > 1 and 𝑥 − 2 < −1 +2 +2 +2 +2 𝑥 > 3 OR 𝑥<1 It is not possible to be greater than 3 and less than 1, so this is an OR inequality. 3 1 15. Solve the inequality and graph your solution on the graph below. |2𝑐 + 3| < 7 To solve absolute value inequalities, we re-write the equation as two equations, without the absolute value sign, and change the way the inequality is facing and the sign on the answer for the second equation. Then we solve the inequalities like normal. 2𝑐 + 3 < 7 and 2𝑐 + 3 > −7 −3 −3 −3 −3 2𝑐 < 4 AND 2𝑐 > −10 2̅ 2̅ 2̅ 2̅ 𝑐 < 2 and 𝑐 > −5 It is possible to be less than 2 and greater than -5, so this is an AND inequality.