Math 131
EXAM 6
FALL 2011
Graph the linear inequality.
6
1) 3y - x 0
5
m=-
6
5
=
3
6 1
2
=
5 3
5
intercept is (0, 0)
Solve the absolute value inequality. Write the solution set using interval notation and graph it.
2 5 - 4x
+ 11 3
2) 3
6
-
2 5 - 4x
3
6
-8
5 - 4x
6
-8-
5 - 4x
6
12
5 - 4x
6
- 12
3
2
5 - 4x - 72
- 4x - 77
77
x
4
(
,-
5 - 4x
6
12
5 - 4x - 72
- 4x 67
67
x 4
67
77
U
, )
4
4
1
3) |2x - 3| - 1 > -3
|2x - 3| > - 2
- ,
Solve the rational inequality using a sign graph. Write the solution set in interval notation and graph it. (10 points)
18
15
>
4)
5-x x+1
18
15
>0
5-x x+1
18 x + 1
15 5 - x
>0
5-x x+1
x+1 5-x
18x + 18
75 - 15x
>0
5-x x+1
x+1 5-x
33x - 57
>0
x+1 5-x
33x - 57 = 0
33x = 57
57
x=
33
x+1=0
x=- 1
5-x=0
5=x
33x - 57
x+1
5-x
------------++++++++++++++++++++++++
----++++++++++++++++++++++++++++++++
++++++++++++++++++++++--------------
- ,- 1 U
57
,5
33
2
Solve the inequality. Graph the solution set on a number line and write the solution set in set-builder notation.
Use a sign graph to determine solution set.
(10 points)
2
5) 4x + 11x - 20 0
4x - 5 x + 4
0
4x - 5 = 0
4x = 5
5
x=
4
4x - 5
x-4
x|x
x+4=0
x=-4
------------------------+++++++++++
---------++++++++++++++++++++++++++
- 4 or x
5
4
Solve the inequality. Give the solution set in both interval and graph forms.
6) -21 < 5a + 4 -1
- 25 < 5a - 5
- 5 < 5a - 1
( - 5, - 1]
For the compound inequality, give the solution set in both interval and graph forms.
2
5
x
x 1
- 2x - 1
7) (1 - x) > (7x - 3) and
3
9
20 2 4
2
5
(9) (1 - x) > (7x - 3)(9)
3
9
6(1 - x) > 5(7x - 3)
6 - 6x > 35x - 15
- 41x > - 21
21
x<
41
- ,
20
x
20
x
x
x
10x - 5 2x - 1
10x - 10x + 5
5
21
41
3
x 1
- 2x - 1 20
2 4
(10 points)
For the compound inequality, give the solution set in both interval and graph forms.
8) -3x + 1 7 or 6x + 3 -21
-3x 6 or 6x - 24
x - 2 or x - 4
- ,
Solve the system of inequalities by graphing.
4 + y > -2x
x y
1
+
9)
4 8
x y
+
4 8
4 + y > - 2x
8
18
y > - 2x - 4
2x + y 8
y - 2x + 8
4
10) 3 - x
9
-x 6
x -6
y
> -1
3
y>- 3
Solve the system of equations using Cramer's Rule.
11) 3x + 5y = 30
7x - 4y = 23
D = 3 5 = - 12 - 35 = - 47
7 -4
Dx = 30 5 = - 120 - 115 = - 235
23 -4
Dy = 3 30 = 69 - 210 = - 141
7 23
x=
- 235
=5
- 47
y=
- 141
=3
- 47
5, 3
5
Solve the system of three linear equations containing three unknowns.
12)
1
- x + 2y - 2z = -16
3
3x -
4
y + z = 26
3
x - 3y + 3z = 27
3-
1
x + 2y - 2z = -16 3
3
- x + 6y - 6z = - 48
1 and 3
- x + 6y - 6z = - 48
x - 3y + 3z = 27
3y - 3z = - 21
3 3x -
4
y + z = 26 3
3
9x - 4y + 3z = 78
1 and 2
9 - x + 6y - 6z = - 48 9
9x - 4y + 3z = 78
- 9x + 54y - 54z = - 432
9x - 4y + 3z =
78
50y - 51z = - 354
4 and 5
-17(3y - 3z) = - 21(-17)
50y - 51z = - 354
3(-3) - 3z = - 21
- 9 - 3z = - 21
x - 3(- 3) + 3(4) = 27
x + 9 + 12 = 27
-51y + 51z = 357
50y - 51z = - 354
- 3z = - 12
z=4
x + 21 = 27
x=6
-y=3
y=- 3
6, - 3, 4
6
Solve the system of equations by graphing.
13) -x + 2y = 4
4x - 8y = 8
- x + 2y = 4
-1 1
m==
2
2
4x - 8y = 8
4
1
m==
-8 2
4
= 2 0, 2
2
8
= - 1 0, - 1
-8
Solve the system of equations using either substitution or elimination.
1
y= x+3
2
14)
x - 2y = -6
substitution
1
x-2 x+ 3 =-6
2
x-x-6=- 6
-6=- 6
x | x - 2y = - 6
7