Answers to Sample Test!
1) a) 7x > 24
x > 24/7
o------------->
24/7
b) Multiply both sides
by 12 to get
8 - 4x < 9 - 6x
2x + 8 < 9
2x < 1
x < 1//2
<-----------] closed dot!
1/2
c) x < -5 or
x > 5
<----------]
[------------->
-5
5
d) -7 < x - 5 <
7
-2 < x < 12
o---------------o
-2
12
e) -23 < 5 -
2x < 23
-28 < -2x < 18
14 > x > -9
[-------------------------]
-9
14
f) 3 < x - 2
< 7 or -3 > x - 2 > -7
5 < x < 9 or -1 > x > -5
[---------]
[-------------]
-5 -1
5
9
2) a) (x - 1)(x - 4) > 0
-
-
+ (x - 4)
-
+
+ (x - 1)
<-----------0-----------0------------->
1
4
We want positive. Answer:
<-----------0
0------------>
1
4
b) (x2 - 1)(x2
+ 1) < 0
(x - 1)(x + 1)(x2 + 1) < 0
+
+
+
(x2 + 1)
-
-
+
(x - 1)
-
+
+
(x + 1)
<---------0------------0-------------------------->
-1
1
We want negative. The answer
is:
0--------------0
-1
1
c)
-
+
+
+ (x + 3)
-
-
+
+ (x - 4)
-
-
-
+ (x - 5)
<---------------[]-------------[]-----------0--------------->
-3
4 5
We want negative: Answer
<----------------]
[-----------0
-3
4
5
d)
The zeros are at -2.6, .8 and 1.7
We want the area to be < 0. We need all
areas of the above graph that are beneath the x-axis.
Answer:
<---------------0
0-----0
-2.6 .8
1.7
e)
The zeros are -1, and .5
We want the area above the x-axis
0-------------------->
.5
3) a)
b)
c)
The area is from -2 to 1 and 5 to 8 exclusive.
The lines are dotted!
4) a)
b)
c)
5)
The corner points are: (0, 0), (0, 2), (2,
1) and (3, 0)
P = 2x + 3y
(0, 0) yields 0
(0, 2) yields 6
(2, 1) yields 7
(3, 0) yields 6
The maximum value is 7 and it happens at (2, 1)
6)
x = amount of corn
y = amount of wheat
constraints
x > 0
y > 0
x + y > 27
x > 2y
objective function: C = 250 x + 350y
The corner points are (18, 9) and (27, 0)
(18, 9) yields 7650
(27, 0) yields 6750
To minimize, take (27, 0)
