Download Unit 3 * Inequalities - Madison Public Schools

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Unit 4 – Inequalities
Study Guide
Introduction to Inequalities
1. Match each phrase on the left with its corresponding symbol on the right.
Phrase
“…is fewer than…”
“…is no more than…”
“…is at least…”
“…is at most…”
“…is more than…"
“…is no less than…”
Symbol
<
>
≤
≥
2. Tell whether -8 is a solution of each inequality.
𝑥
b. 2 < −4
a. x + 15 ≥ -10
3. Write an inequality for each graph below. Then, write a second, equivalent inequality.
a.
b.
4. Write the word sentence as an inequality.
a. A number y is no more than -8
b. A number w added to 2.3 is more than 18.
2
c. A number t multiplied by -4 is at least − 5 .
d. A number b minus 4.2 is less than -7.5.
Solve and graph each inequality below.
One and Two-Step Inequalities
5. 3 + x < 10
6. 24 ≤ 9 – x
7. 7x ≥ 56
8. − 6 < 6
9.
𝑥
4
3
+ 4 < 15
11. 3y – 7 > 17
𝑥
𝑥
10. 4 – 8 > 15
12. -20x - 5 > 5
13. John is selling cupcakes to raise money for charity. For each cupcake sold, John earns $.80. How many
cupcakes would John have to sell if he wants to donate at least $50.00 to charity? Write an inequality
and solve. Be sure to express your answer with the correct units.
Let x =
14. A small airplane can hold 44 passengers. Fifteen passengers board the plane. Write and solve an
inequality that represents the additional number of passengers that can board the plane.
Let x =
b. Can 30 more passengers board the plane? Explain.
Solve and graph each inequality below. When possible, note if there are no solutions or infinite solutions.
Multi-Step Inequalities
15. 8(3g – 2) ≤ 12(2g + 1)
16. 4 – 7(x – 1) ≤ 2(x – 8)
17. 2x – (5x + 11) > 4x + 17
18. 6(2x – 1) ≥ 3(4x + 1)
19. The perimeter of the rectangle is at least 12 inches. The area is no more than 27 inches. Write and
solve an inequality for each condition. Give two possible values for x.
20. An isosceles triangle has a base of 5 centimeters and legs x centimeters long. The perimeter is no more
than 30 centimeters. Write and solve an inequality to find the possible values of x.
21. The 7th grade is going on a field trip and the students need to raise at least $720 in order to pay for the
trip. They decide to sell T-shirts to raise money, and will make $12 toward the trip for every T-shirt
they sell. If they currently have $240, write and solve an inequality to find out how many shirts they
will need to sell to have enough money to go on their trip.
Compound Inequalitiesp
Find the set of solutions that would make satisfy each inequality. Graph each solution set.
22.
2r + 3 < 7 or –r + 9 ≤ 2
23.
6 < x + 5 ≤ 11
24.
-12 < 2(4x + 16) < 18
25.
-14 > w + 3 or 3w ≥ -27
1
Answer Key
1.
< “…is fewer than…”
≤ “…is no more than…”
≥ “…is at least…”
≤ “…is at most…”
> “…is more than…"
≥ “…is no less than…”
2. a. Yes, -8 is a solution
b. No, -8 is not a solution
3. a. x > 12
b. x ≤ -4
4. a. y ≤ -8
b. 2.3 + w > 18
2
c. -4t ≥ − 5
d. b – 4.2 < -7.5
5. x < 7
6. x ≤ -15
7. x ≥ 8
8. x > -36
9. x < 57
10. x > 92
11. y > 8
1
12. x < − 2
13. Let x = Number of cupcakes John has to sell to raise $50
.80x ≥ 50
John has to sell at least 63 cupcakes
14. Let x = number of additional passengers that can board the plane
x + 15 ≤ 44
No more than 29 passengers can board the plane.
b. No, only 29 or fewer passengers can board the plane and 30 > 29.
15. All real numbers
16. x ≥ 3
17. x < 4
18. No solutions
19. Perimeter: 2x + 6 ≥ 12
Area: 3x ≤ 27
Example answer: 4 and 5
x can be any number greater than or equal to 3 and less than and equal to 9
3≤x≤9
20. 5 + 2x ≤ 30
x ≤ 12.5 cm
21. Let x = how many shirts the 7th grade needs to sell
12x + 240 ≥ 720
40 shirts
22. r < 2 or r ≥ 7
23. 1 < x ≤ 6
24. -10 < x < 5
25. w < -17 or w ≥ -9