Question

write <, =, or > to make a true sentence.

1. 65? 60
2. -7? 7
3. |-9|? 9
4. 11? -|-11|
5. -6 + 5? -5 + 7
6. 8 + (-11)? 9 + (-7)
7. 2 - 2? 0 - 1
8. 1 - 5? 0 - (-3)
9. -3•(-3)? 3•3
10. 12(-6)? 13(-5)
11. 24÷6? 14÷7
12. -6÷(-2)? 6÷(-2)
13. |-6| + 2? |-6 + 2|
14. |-4| - |-5|? |-4 + 5|
15. |3(-4)|? |3|•|-4|

tell whether the inequality is true or false for each given value.

1. m + 10 ≠ 55, when m = 15

substitute 15 for m
15 + 10 ≠ 55; 25 ≠ 55; true

1. p - (-40) < 52 when p is -18
2. -3a > 5, when a = -2
3. d÷(-3) ≥ -3 when d is -9
4. c² + 14 < 15 when c is -5
5. x - |-9| > 3 when x = 0

problem solving
write and simplify an inequality using ≤ or ≥, then answer each question.

1. cameron has a summer job selling magazine subscriptions. he earns $4 for each subscription he sells. he hopes to earn at least $100 over the summer. if he sells 26 subscriptions, will he meet his goal?
2. zoe’s father told her she could invite no more than 12 people to her birthday party. she has 6 people she wants to invite for sure. if she invites 7 more, will she be within the limit her father set?

spiral review

1. use mental math to evaluate each expression.

a. 3(-9)
b. -27÷9
c. 27÷(-9)
d. -27÷(-9)
e. 7 - 8
f. -3 + (-5)

Explanation:

Step1: Solve 21.

Since 65>60, the symbol is >.

Step2: Solve 22.

-7 is less than 7, so the symbol is <.

Step3: Solve 23.

| - 9| = 9, so the symbol is =.

Step4: Solve 24.

-| - 11|=-11, and 11 > - 11, so the symbol is >.

Step5: Solve 25.

-6 + 5=-1, -5 + 7 = 2, -1<2, so the symbol is <.

Step6: Solve 26.

8+( - 11)=-3, 9+( - 7)=2, -3<2, so the symbol is <.

Step7: Solve 27.

2 - 2 = 0, 0 - 1=-1, 0>-1, so the symbol is >.

Step8: Solve 28.

1 - 5=-4, 0-( - 3)=3, -4<3, so the symbol is <.

Step9: Solve 29.

-3×(-3)=9, 3×3 = 9, so the symbol is =.

Step10: Solve 30.

12×(-6)=-72, 13×(-5)=-65, -72<-65, so the symbol is <.

Step11: Solve 31.

24÷6 = 4, 14÷7 = 2, 4>2, so the symbol is >.

Step12: Solve 32.

-6÷(-2)=3, 6÷(-2)=-3, 3>-3, so the symbol is >.

Step13: Solve 33.

- 6

+2=6 + 2 = 8,

-6 + 2

=

- 4

= 4, 8>4, so the symbol is >.

Step14: Solve 34.

- 4

-

- 5

=4 - 5=-1,

-4 + 5

=

1

= 1, -1<1, so the symbol is <.

Step15: Solve 35.

3×(-4)

=

- 12

= 12,

3

×

- 4

=3×4 = 12, so the symbol is =.

Step16: Solve 36.

Substitute m = 15 into m + 10≠55, 15 + 10 = 25, 25≠55, True.

Step17: Solve 37.

Substitute p=-18 into p-( - 40)<52, -18 + 40 = 22, 22<52, True.

Step18: Solve 38.

Substitute a=-2 into -3a>5, -3×(-2)=6, 6>5, True.

Step19: Solve 39.

Substitute d=-9 into d÷(-3)≥ - 3, -9÷(-3)=3, 3≥ - 3, True.

Step20: Solve 40.

Substitute c=-5 into c²+14<15, (-5)²+14=25 + 14 = 39, 39>15, False.

Step21: Solve 41.

Substitute x = 0 into x-| - 9|>3, 0 - 9=-9, -9<3, False.

Step22: Solve 42.

Let the number of subscriptions be s. The inequality is 4s≥100. If s = 26, then 4×26 = 104, 104≥100, Yes, he will meet his goal.

Step23: Solve 43.

Let the total number of people be n. The inequality is n≤12. She has 6 people and wants to invite 7 more, so n=6 + 7 = 13, 13>12, No, she will not be within the limit.

Step24: Solve 44a.

3×(-9)=-27.

Step25: Solve 44b.

-27÷9=-3.

Step26: Solve 44c.

27÷(-9)=-3.

Step27: Solve 44d.

-27÷(-9)=3.

Step28: Solve 44e.

7 - 8=-1.

Answer:

1. >
2. <
3. =
4. >
5. <
6. <
7. >
8. <
9. =
10. <
11. >
12. >
13. >
14. <
15. =
16. True
17. True
18. True
19. True
20. False
21. False
22. Inequality: 4s≥100, Yes
23. Inequality: n≤12, No

44a. -27
44b. -3
44c. -3
44d. 3
44e. -1