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Algebra 2
Test #3 – Solving Inequalities
October 31, 2007
NAME: __________________
1.
Multiple Choice -- circle the correct option letter for each.
(a)
Which system of inequalities is best represented by the region shaded in the graph below?
[2]
(A)
(b)
(B)
(C)
(D)
x 1
?
y  8
Which graph correctly represents the system of inequalities 
(A)
(B)
(C)
(D)
[2]
(c)
y  x 1
Which graph correctly represents the system of inequalities 
?
 y 1
(A)
(B)
(C)
(D)
[2]
(d)
Which of the following represents the solution set of | m | 10 ?
(A)
The solution set is {m | m
10 or m 10}.
(B)
The solution set is {m | m < 10 or m > 10}.
(C)
The solution set is {m | m < 10 or m > 10}.
(D)
The solution set is {m | m < 10 or m > –10}.
[2]
(e)
Which inequality has the solution set graphed below?
[2]
(A)
x  3  3
(B)
x 3
(C)
x 3
(f)
Which inequality has the set of all real numbers as its solution set?
[2]
(A)
2.
Solve the following and graph the solution set on the given number line.
(a)
3  x  1
(B)
3  4x  7
3 x 1
(b)
3 x 1
x 3
(D)
3 x  0
4  n 1  7n  8
0
0
(c)
(C)
(D)
3x  2  13 or 6x  4  14
(d)
11  2g  7 and 3g  5  17
[16]
0
0
(e)
9  2z  7  10
0
(f)
5m  8  10  m or 5m 11  9
0
3.
Solve the following absolute value inequalities and graph the solution set on the given number line.
(a)
14  w  20
(b)
2 y  9  3  19
[8]
0
4.
0
In order to score an A for the semester, a student must have an average of at least 90%. If Peter
scored 85, 92, and 86 on his three tests, how much will he need to score on the exam if the exam is
worth twice as much as a test (i.e one exam is equivalent to two tests)? You are expected to use
inequalities in your solution.
[4]
5.
Write a system of inequalities that describes the shaded region shown below.
[3]
6.
[5]
By using the fact that the area of a triangle is A  12 bh , find the area of the shaded region in #5.
7.
A shoe manufacturer makes outdoor and indoor soccer shoes. There is a two step manufacturing
process for both kinds of shoes. Each pair of outdoor shoes requires 2 hours of processing in step
one and 1 hour in step two. Indoor shoes require 1 hour of processing in step one, and 3 hours in
step two. The company has only 40 hours available for step one and 60 hours available for step
two. Outdoor shoes make a profit of $20 per pair and indoor shoes make a profit of $15 per pair.
How many pairs of each shoe should be made to maximize profit? What is the maximum profit?
Use the graph paper provided in your solution – choose an appropriate scale!
[12]
y
x
[60] Total
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