Download 3 - YES b. –1

Algebra I
UNIT 2 REVIEW
Cierech/Dahl
Name:
Date:
Is each number a solution of the given inequality?
1. 4y + 3 ≤ –7
a. –3 - YES
b. –1 - YES
c. 3 - NO
2. –6x + 2 > 5
a. –3 - YES
b. 4 - YES
1
2
c. –0.5 - NO
Write an inequality to model each situation.
3. The high temperature will be at least 75°F today.
x ≥ 75
4. The class can contain at most 28 students.
x ≤ 28
Write an inequality for each graph.
5. 6.
x ≥ -3.5
x < -1
Solve each inequality. Graph the solution.
7. |r + 3| ≥ 7
8. |6q + 9| ≤ 9
r ≥ 4 or r ≤ -10
9. –20 ≤ 5y
-3 ≤ q ≤ 0
10. –9 < 3n < 18
y≥-4
11. –3 < 5c + 7 < 22
-2 < c < 3
13. 4 – x > 3
x<1
15. f ≥ –5f + 36
f ≥6
-3 < n < 6
12. –6b > 42 or 4b > –4
b < -7 or b < -1 So b < -1
14. 6y – 8 ≤ 10
y ≤ 3
3
16.  x  24
5
x > -40
17. 3x – 8 < –2x + 22
x<6
18. 2| d + 5 | – 1 < 3
-7 < d < -3
Solve each inequality. Check your solution.
19. 3(x – 4) < –15
x < -1
21. 7x + 2(3x – 11) ≤ 17
x≤3
20. 2(5y + 13) – 5.7 < 20.3
y<0
22. 6(x – 11) – 4x < –72
x < -3
Write a compound inequality that each graph could represent.
24.
25.
-1 ≤ x < 3
x < 0 or x > 2
Solve each equation. Check your solutions.
26. | 5x + 13| = –7
27. 2 = | w – 13|
NO SOLUTION
28. | 4x + 1| – 3 = 26
w = 11 or 15
29. 5| 8 – y | = 30
x = -7.5 or 7
y = 2 or 14
30. Suppose you are working for a trucking company. Your job is to load a truck
with at least 5000 lb of freight. You have loaded 2395 lb of freight, but you have
to unload 50 lb that was loaded by mistake. Write and solve an inequality to
find how many more pounds you need to load.
2395 – 50 + x ≥ 5000; x ≥ 2655 lbs.
31. The art club is sponsoring four art shows. They hope the average attendance for the four shows will be
between 100 and 120, inclusive. The attendance for the first three shows was 100, 105, and 91. What possible
attendance numbers for the fourth show will allow them to reach their goal? Write and solve an inequality for
this situation.
100 ≤ (296+x)/4 ≤ 120; 104 ≤ x ≤ 184
32. A box of cereal should weigh 397 g. The quality control inspector weighs every fiftieth box. The inspector
rejects any box that is not within 10 g of the ideal weight. Find the range of acceptable weights. Write and
solve an absolute value inequality for this situation.
| x – 397 | ≤ 10; 387 ≤ x ≤ 407
33. Writing Explain how to solve | 2d | + 3 < 7.
First, you would subtract 3 from both sides of the inequality, giving you | 2d | < 4. Next, you
Would set up a compound inequality 2d < 4 AND 2d > -4. (You could also set up the compound
Inequality -4 < 2d < 4.) Next, you would divide both side of 2d < 4 by 2 yielding d < 2, and divide both
Sides of 2d > -4 by 2 yielding d > -2. Finally, you would write your solution as a compound inequality
-2 < d < 2.