Math 093
Final Review 1
Solve the following equations or inequalities:
1.
2  x  4  4 x   x  3
2.
4
 3x  15  16
3
3.
3  2x  19  4 x
4.
1
5.
The sum of three consecutive even integers is 480. Find the third integer.
2x x

5 10
Simplify the following:
6.
 5x 
6 3
Multiply and simplify completely, if possible:
2 x  5 x 2  2 x  1
8.
10.
11.
 5xy  3x
Add:
2
 x  1  x  1
9.
 2 x  3 2 x  3
8
5
y 2  4 y 2   6x2 y  2x2 y 2  4 y 2 
 49 x
Divide:
7.
4
 14 x3  56 x 2 
7x 
2
Simplify the following (No negative exponents in the answers)
12.
 2x
3
y 3
13.
2 xy 3
 x3 y 5 
 2 
 z 
3
Factor the following completely:
14.
x2  9
15.
3x3  27 x
16.
5 x 2  23x  10
17.
3x 2  5 x  2
Solve the following:
x  x  4  32
18.
x 2  2 x  15  0
19.
21.
List all numbers for which
x5
is undefined
x 2  25
20.
13 1 1
 
x 10 3
For the following, performed the indicated operation and simplify, if possible:
x  10 x  5
x 2  16 6 x
x2  4
x2


 2
22.
23.
24.
x 3 3 x
4x 4  x
x 1 x  2x  3
25.
5
1

x4 x
Math 093
Final Review 1
Graph the following and label the points:
5 x  2 y  10
26.
27.

4  a solution for the equation:

y  2x 1
28.
 1
Is   ,
 2
29.
Find the slope of the line containing the following points: (– 8,– 2) and (– 4, – 6)
30.
Write the slope–intercept equation for the line that has a slope of –3 and y–intercept (0, 2)
31.
Solve by inspecting the slope and y-intercept, state the type of system and number of solution:
x  y  7

3x  y  9
x  2y  5
Solve by any method, state the type of system and number of solution:
32.
2

x  y  3
3

3 x  2 y  4
33.
x  y  2

2 x  3 y  1
34.
2 x  y  5

2 y  4 x  10
34.
Mickey found 20 coins in his piggy bank, all in quarters and nickels. He counted the change
and found that he had $ 3.40. How many of each coin did he have?
35.
Tommy invested $ 6,000 in two different stocks. Part of his money was invested in Bank A
which earned 6% interest, and the other part earned 4% interest in Bank B. How much was
invested in each stock if he made $ 290 in interest?
Simplify the following completely, assume all variables are positive:
37.
50
40.
90  4 40
38.
7 x3 y  21x 2 y 3
41.

2 x 2  18
5 2

39.
2
100
64
42.

45.
 x  2
52

Solve the following for x:
43.
2x 1  1
44.
46.
x 2  2 x  35
47.
49.
Solve for x by completing the square only:
50.
Find the square roots of 25
1 x  x 1
48.
x2  4x  6  0
2
1
5x  1  0
5 2

Math 093
Final Review 1
SOLUTIONS
8
3
3.)
x
(x-1)13
8.)
10x3 -4x2 + 2x
10.)
5xy + x2y2 +6x2y
11.)
7x2 – 2x + 8
12.)
1
16 x 4 y 6
13.)
z6
x9 y15
14.)
(x – 3)(x + 3)
15.)
3x (x – 3)(x + 3)
16.)
(5x + 2)(x – 5)
17.)
(3x - 2)(x – 1)
18.)
5, -3
19.)
8, -4
20.)
30
21.)
5, -5
22.)
3( x  4)
2
23.)
(x – 2)(x – 3)
24.)
2 x  15
x3
25.)
6x  4
x ( x  4)
28.)
no
29.)
-1
30.)
y = -3x + 2
31.)
(4, -3)
32.)
no solution
33.)
(-1,1)
34.)
infinite solutions
34.)
12Q, 8 N
35.)
$2500@6% , $3500@4%
37.)
5 2
38.)
7 x 2 y 2 3x
39.)
10/8
40.)
11 10
41.)
94 5
42.)
1
43.)
2
44.)
3, -3
45.)
3, 1
46.)
7, -5
47.)
0, -1
48.)
no solution
49.)
2  10
50.)
5, -5
1.)
x = -11
2.)
x=1
4.)
x≤2
5.)
158,160,162
6.)
-125x18
7.)
9.)
4x2 – 9