Math 131
EXAM 3
Fall 2011
Solve. If the equation is an identity or contradiction, then indicate so.
3
7
1
1) - y - (y + ) = ( y + 1)
5
9
6
90 -
3
7
1
y - (y + ) = ( y + 1)90
5
9
6
- 54y - 90y - 70 = 15y + 15
- 144y - 70 = 15y + 15
- 85 = 159y
85
=y
159
-
85
159
Solve the equation.
2) 3(x - 1) = 15x + 3(x 2 + 2)
3x - 3 = 15x + 3x 2 + 6
0 = 3x 2 + 12x + 9
0 = x 2 + 4x + 3
0= x+3 x+1
x+3=0
x=- 3
x+1=0
x=- 1
-3, -1
3) 2x 1/2 - 3x 1/4 - 2 = 0
2x 1/4 + 1 x1/4 - 2 = 0
2x 1/4 + 1 = 0
2x 1/4 = - 1
x1/4 - 2 = 0
x1/4 = 2
x1/4 = -
x = 24
1
2
x = 16
16
1
4) 2(x + 5) 2 - 13(x + 5) = - 18
2(x + 5) 2 - 13(x + 5) +18 = 0
2(x + 5) - 9 (x + 5) - 2 = 0
2x + 10 - 9 x + 3 = 0
2x + 1 x + 3 = 0
2x + 1 = 0
x+3=0
2x = - 1
x=- 3
x=-
-
1
2
1
,- 3
2
5) 4x -2 + 12x -1 + 9 = 0
2x -1 + 3 2 = 0
2x -1 + 3 = 0
2x -1 = - 3
x-1 = -
x=-
-
3
2
2
3
2
3
6) x3 - 4x 2 - 25x + 100 = 0
x2 x - 4 - 25 x - 4 = 0
x 2 - 25 x - 4 = 0
x2 - 25 = 0
x2 = 25
x=±5
x-4=0
x=4
± 5, 4
2
7) 16 - 81y4 = 0
16 = 81y4
16
= y4
81
±
4
16
=y
81
y=±
8)
2
3
1
4
-2
+
=
2
2
2
z + 2z - 35 z - 25 z + 12z + 35
1
4
-2
+
=
z-5 z+7
z-5 z+5
z+5 z+7
z+5 z+7 z-5
1
z-5 z+7
+
4
z-5 z+5
=
-2
z+5 z+7 z-5
z+5 z+7
z+5+4z+7 =-2z-5
z + 5 + 4z + 28 = - 2z + 10
5z + 33 = - 2z + 10
7z = - 23
z=-
-
23
7
23
7
Solve the absolute value equation.
9) |-10x - 7| = |-5 + 7x|
- 10x - 7 = - -5 + 7x
- 10x - 7 = 5 - 7x
- 12 = 3x
- 10x - 7 = -5 + 7x
- 2 = 17x
2
=x
17
-4=x
- 4, -
2
17
3
10) -
-
4 2
1
x+
+ 19 = 11
5 9
6
4 2
1
x+
=- 8
5 9
6
2
1
5
x+
=- 8 9
6
4
2
1
x+
= 10
9
6
2
1
x + = 10
9
6
18
2
1
x+
= 10(18)
9
6
4x + 3 = 180
4x = 177
177
x=
4
2
1
x + = - 10
9
6
18
2
1
x+
= -10(18)
9
6
4x + 3 = - 180
4x = - 183
183
x=4
177
183
, 4
4
Solve the equation.
11) 3x - 1 + 17 = 10
3x - 1 = - 17
12)
x2 - 2 + x = 4
x2 - 2 = 4 - x
2
x2 - 2 = 4 - x 2
x2 - 2 = 16 - 8x + x 2
8x = 18
18
x=
8
x=
9
4
9
4
13) 11 = 15 + (12 - x)1/3
- 4 = (12 - x)1/3
-4 3 = (12 - x)1/3 3
- 64 = 12 - x
76 = x
76
4
14)
5
9 - 5x +
5
-7 + 6x = 0
3
9 - 5x = - -7 + 6x
3
3
3
3
9 - 5x = - -7 + 6x
9 - 5x = - - 7 + 6x
9 - 5x = 7 - 6x
x = -2
3
-2
Solve the equation by using the square root method.
15) 12(a + 5)2 + 6 = 0
12(a + 5)2 = - 6
6
(a + 5)2 = 12
Solve the equation by completing the square.
16) -2x 2 + 3x - 9 = 0
-2x 2 + 3x = 9
x2 -
3
9
x=2
2
x2 -
3
9
72
9
x+
=+
2
16
16 16
x-
3 2
63
=4
16
5
Solve the problem by first writing an equation relating all of the variable.
17) If f varies jointly as h and the square root of q, and f = -96 when q = 4 and h = 3,
25
9
find f when q =
and h =
.
144
20
f = kh q
- 96 = k 3
4
f = - 16
9
20
9 5
20 12
-
96
=k
3 4
f = - 16
-
32
=k
2
f=- 3
25
144
- 16 = k
18) The volume V of a given mass of gas varies directly as the temperature T and inversely as the pressure P. If V =
490.0 in.3 when T = 350° and P = 10 lb/in.2 , what is the volume when T = 170° and P = 20 lb/in. 2?
V=
kT
p
490 =
k 350
10
490 10
=k
350
V=
14 170
20
V = 119
14 = k
6