093 Final Review 2
Solve the following equations or inequalities:
13 1 1


1.
2.
8x  5  x  3  20
x 10 3
3. 3  2x  19  4x
4.
The sum of three consecutive even integers is 234. Find the
integers.
Simplify the following:
5.
 2xy 
4 5
6.
Multiply and simplify completely, if possible:
x  3 x 2  3x  1
7.
8.


9.
Subtract and combine like terms:
 3xy  2 x2 y 2  6 x 2    5x 2 y  3x 2 y 2  6 x 2 
10.
Add:
11.
Divide:
7x
3
 
 5x2  3  8x2  4 x  9
18x y
3
3
9
 2 x  1 2 x 1

35 x  30  10 x 2
14.
x2  8x
3x 2  7 x  4
Solve the following for x:
x 2  x  72  0
16.
18.
5
 36 x3 y 5  9 x3 y 4   9 x3 y 4
Factor the following completely:
x2  4 x  3
12.
13.
15.
 x  2  x  2
17.
List all numbers for which
x  x  3  54
x 2  4 x  21
is undefined
x 2  3x  18
For the following, performed the indicated operation and simplify, if
possible:
x  12 x  11
x 2  64 6 x
x 2  49 7  x



19.
20.
21.
x5 5 x
4x 8  x
2x
38 x
22.
Is  2, 3 a solution to:
2 x  5 y  10?
093 Final Review 2
Graph the following and label at least two points on your graph:
1
y   x 1
5 x  3 y  15
23.
24.
3
25. Find the slope of the line that passes through the points (9, 7) and
(5,4)
2 x  5 y  11

7 x  4 y  2
26.
Is (–3, –1) a solution to the system of equations:
27.
Solve by inspecting the slope and y-intercept, state the type of
x  y  5
system and number of solution:

3x  y  7
Solve by any method, state the type of system and number of solution:
28.
2 x  y  2

2 x  3 y  22
29.
1

2 x  y  4
2


4 x  y  12
31.
x  3y  0

2 x  4 y  10
32.
2 x  3 y  11

4 x  6 y  13
2 x  y  5
30. 
3x  5 y  4
33.
Tim has $16.30 in quarters and nickels. If he has 98 coins
together, how many quarters and nickels does he have?
34.
Henry invested $18,000 in two banks. He received $1080 in
interest. How much did he invest in each bank if the first bank
pays 5% interest and the second bank pays 7% interest?
Simplify the following completely, assume all variables are positive:
35.
50
72
38.
35 x 4 y 2  21x 5 y 3
36.
6 7
37.

5 2

52

093 Final Review 2
Solve the following for x:
39.
4 x  7  15
42.
x  5  x 1
40.
 x  3
2
1
41.
 x  5
2
43.
Solve for x by completing the square only: x 2  8 x  13  0
44.
Solve for x by using Quadratic formula:
45.
Find the square roots of 9
x 2  4 x  2
5  2
093 Final Review 2
SOLUTIONS
1.
x = 30
2.
x
5
3
3.
x
8
3
4.
76, 78, 80
5.
 32 x 5 y 20
6.
x  2 14
7.
x 3  6 x 2  10 x  3
8.
4x 2  1
9.
3xy  5 x 2 y 2  5 x 2 y
10.
7 x 3  3x 2  4 x  6
11.
2
 4y 1
y
12.
x  3x  1
13.
52x  3x  2
14.
xx  8
15.
3x  4x  1
16.
x  9, x  8
17.
x  6, x  9
18.
x  3, x  6
19.
3 x  8
2
20.
19x  7
21.
2 x  23
x5
22.
No
23.
graph
24.
graph
093 Final Review 2
3
4
25.
m
26.
No
27.
one solution
28.
2,  6
29.
No solution
30.
3,  1
31.
(15, 5)
32.
No solution
33.
57 quarters;
41 nickels
34.
$9,000 @ 5%;
$9,000 @ 7%
35.
5
6
42
36.
37.
1
38.
7 x 4 y 2 15xy
39.
x = 16
40.
x = 2, x = 4
41.
x  5 7
42.
x=4
43.
x  4  3
44.
x  2 2
45.
3 and -3