Test 1
Name:
Find all values of x satisfying the given conditions.
1) y1 = 8x + 4(1 + x), y2 = 3(x - 8) + 10x, and y1 = y2
A) {-28}
B) {-9}
Find all values of x such that y = 0.
2) y = 2[2x - (3x - 9)] - 4(x - 9)
A) {-9}
B) {9}
Solve the equation.
x x
3) = + 8
5 6
A) {30}
4)
2x x
= +4
5
3
A) {-120}
B) {48}
C) {9}
D) {28}
C) - 3
D) 3
C) 240
B) {60}
D) {40}
C) {-60}
D) {120}
First, write the value(s) that make the denominator(s) zero. Then solve the equation.
4
3
12
5)
+
=
x + 2 x - 2 (x + 2)(x - 2)
A) No restrictions; {2}
C) x ≠ -2, 2; {3}
A) ∅
B) {0}
C) {3}
2)
3)
4)
5)
B) x ≠ -2; {2}
D) x ≠ -2, 2; ∅
Solve the equation.
1
2
-2
6)
+
=
x+5 x+3
x2 + 8x + 15
1)
D) {-5}
Determine whether the equation is an identity, a conditional equation, or an inconsistent equation.
7) 5(4x - 35) = 20x - 175
A) Identity
B) Conditional equation
C) Inconsistent equation
8) 6x + 8x = 13x
A) Identity
B) Conditional equation
C) Inconsistent equation
9) -3(x + 3) + 87 = 5x - 8(x - 6)
A) Identity
B) Conditional equation
C) Inconsistent equation
6)
7)
8)
9)
Use the five-step strategy for solving word problems to find the number or numbers described in the following exercise.
10) When four times the number is added to 8 times the number, the result is 48. What is the number?
10)
A) -6
B) 6
C) 4
D) 0.7
11) When 5 times a number is subtracted from 7 times the number, the result is 20. What is the
number?
A) -10
B) 0.4
C) 2
D) 10
1
11)
Add or subtract as indicated and write the result in standard form.
12) (2 - 5i) + (8 + 7i)
A) 10 - 2i
B) -6 + 12i
C) -10 - 2i
13) (4 + 5i) - (-7 + i)
A) 11 + 4i
B) -11 - 4i
C) -3 + 6i
14) (-3 - 3i) + (-6 - 5i) + (4 - 5i)
A) -5 - 13i
B) 7 - 3i
C) -9 - 8i
Perform the indicated operations and write the result in standard form.
15) -25 + -81
A) 45i
B) -14
C) 14i
16)
-7 - -121
A) 7i - 11
B) i( 7 - 11)
Find the product and write the result in standard form.
17) (4 + 5i)(2 - 8i)
D) 10 + 2i
D) 11 - 4i
D) -13 - 3i
D) -14i
C) i( 7 + 11)
D)
7i - 11i
A) -32 + 42i
B) 48 + 22i
C) 48 - 22i
D) -40i2 - 22i + 8
18) (6 - 4i)(-4 - 5i)
A) -4 - 46i
B) -4 - 14i
C) -44 - 14i
D) -44 - 46i
19) (-6 + i)(-6 - i)
A) 36
B) 37
C) -35
D) -6
Divide and express the result in standard form.
9
20)
7+i
A)
21)
7 + 4i
4 - 7i
22)
8 + 7i
9 - 6i
63
9
i
+
50 50
A) i
A)
10 37
i
+
39 39
Solve the equation by factoring.
23) x2 = x + 6
A) {2, 3}
B)
21
3
i
+
16 16
C)
B) -1
B)
63
9
i
50 50
C) 1
38 37
i
+
15 45
C)
B) {-2, -3}
38
5
i
13 13
C) {-2, 3}
2
D)
21
3
i
16 16
D) -i
D)
2 37
i
+
9 45
D) {1, 6}
12)
13)
14)
15)
16)
17)
18)
19)
20)
21)
22)
23)
24) 9x2 + 18x + 8 = 0
2
1
A) - , 9
2
2 4
B)
,
3 3
2
4
C)
,3
3
2
4
D) - , 3
3
2
2
B)
,9
9
2
C) 0,
9
2
D) - , 0
9
B) {0, 4}
C) {-2, 2}
D) {6}
27) (2x - 5)2 = 25
A) {0, 5}
B) {-5, 0}
C) {-10, 0}
D) {0, 10}
28) 2(x - 4)2 = 4
A) {-4 ± 2}
B) {2, 6}
C) {-6, -2}
D) {4 ±
25) 9x2 - 2x = 0
A) {0}
Solve the equation by the square root property.
26) (x - 2)2 = 4
A) {-4, 0}
Solve the equation by completing the square.
29) x2 - 12x + 11 = 0
A) {-11, -1}
B) {1, 11}
C) {-
30) x2 + 4x - 9 = 0
A) {2 + 13}
C) {-2 - 1 13 , -2 + 1 13}
B) {-2 D) {-1 -
31) 5x2 - 2x - 2 = 0
-1 - 11 -1 + 11
A)
,
5
5
C)
1-
5
11 1 +
,
5
B) -2,
11
D)
Solve the equation using the quadratic formula.
32) x2 + 3x - 54 = 0
A) {9, 6}
B) {-6, 9}
11}
13 , -2 +
13 , -1 +
B)
-4 - 2 -4 + 2
,
4
4
D)
3
25)
26)
27)
2}
D) {1, 10}
28)
29)
30)
13}
13}
31)
12
5
5 - 11 5 + 11
,
25
25
C) {-9, 6}
33) 2x2 + 8x + 7 = 0
-4 - 2 -4 + 2
A)
,
2
2
C)
11,
24)
-8 - 2 -8 + 2
,
2
2
-4 - 30 -4 + 30
,
2
2
D) {-9, 1}
32)
33)
Solve the polynomial equation by factoring and then using the zero product principle.
34) 2x3 + 5x 2 = 8x + 20
A) {-2, 2}
B) -
35) x3 - 9x 2 + 18x = 0
A) {3, 6}
5
,0
2
C) -2, -
B) {-3, -6}
C) {0, -3, -6}
Solve the radical equation, and check all proposed solutions.
36) 7x - 6 = 6
37)
A) {6}
B)
20x - 20 = x + 4
A) {7}
B) {6}
5
,2
2
∅
4
B)
,4
3
5
,2
2
D) {0, 3, 6}
30
C)
7
D) {36}
C) {-5}
D) {-6}
Solve the absolute value equation or indicate that the equation has no solution.
38) 3 x - 3 = 18
A) {3}
B) {3, -9}
C) {9, -3}
39) 3x + 8 + 9 = 13
4
A) - 4, 3
D) -
3
1
C) {- , - }
2
2
D) ∅
D) ∅
34)
35)
36)
37)
38)
39)
Solve the linear inequality. Other than ∅, use interval notation to express the solution set and graph the solution set on a
number line.
40) 5x - 7 > 4x - 2
40)
A) (5, ∞)
-2
-1
5
6
7
8
9
10 11 12
-16 -15 -14 -13 -12 -11 -10 -9
-8
-7
-6
-5
-4
-2
-1
0
1
2
3
4
5
6
7
8
9
10 11 12
-2
-1
0
1
2
3
4
5
6
7
8
9
10 11 12
B) (-9, ∞)
0
1
2
3
4
C) (- ∞, 5]
D) [5, ∞)
-3
4
-2
41) 18x - 18 > 6(2x - 4)
41)
A) [-1, ∞)
-8
-3
-2
-1
0
1
2
3
4
5
6
-14 -13 -12 -11 -10 -9
-8
-7
-6
-5
-4
-3
-2
-1
0
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
B) (-7,
-7
∞)
-6
-5
-4
C) (- ∞, -1)
D) (-1, ∞)
5
Answer Key
Testname: UNTITLED1
1) D
2) B
3) C
4) B
5) D
6) A
7) A
8) B
9) C
10) C
11) D
12) D
13) A
14) A
15) C
16) B
17) C
18) C
19) B
20) C
21) A
22) A
23) C
24) D
25) C
26) B
27) A
28) D
29) B
30) B
31) C
32) C
33) A
34) C
35) D
36) A
37) B
38) C
39) A
40) A
41) D
6