Algebra 1
Name___________________________________ ID: 1
Assignment
Date________________ Period____
Simplify each expression.
1) −
3)
32x 5
16x 4
48n 2
32n 4
5) −
18v 2
12v 3
2)
90n 3
40n 2
4)
10x
20x 2
6)
5x 2 + 3x − 8
8x 2 − 8x
12m + 28
12m + 12
7)
5x 2 + 8x − 21
3x 2 + 9x
8)
9)
20k 2 + 4k
28k 2 − 8k
10)
5a 2 + 28a − 12
4a + 24
12)
18r + 45
1
⋅
8
2r + 5
11)
n − 5 15n 2 − 36n − 27
⋅
5n + 3
3n − 9
13) (2n 2 − 19n + 42) ⋅
7n + 1
14n − 47n − 7
2
14) (2m − 9) ⋅
m+6
2m − 13m + 18
2
15)
5v 2 − 8v − 21
1
⋅
5v + 7
v−8
16)
27 p − 9
9
÷
3p − 1
p−2
17)
8
1
÷ 2
2
15n − 12n 5n − 29n + 20
18)
7n 2 − 7
1
÷
2
21n + 28n − 49 3n + 7
19)
m+2
m−5
÷
18m + 45 18m + 45
20)
18a − 81
1
÷
2
14a − 79a + 72 7a − 8
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Solve each equation. Remember to check for extraneous solutions.
21)
1
1
1
+
=
4 4n 2n
22) 1 =
23)
2 5
= +1
a a
24)
6
1
=1−
b
b
25)
1
n−2 1
−
= 2
2
4n
2n 2
n
26)
5
1
=1−
4m
4m
27)
m−1
1
=1+
3m
3m
28)
1
1
1
− =
5x
2 10x
30)
5
4
1
= 2
+
n − 5n n − 5n n
29) 1 +
6 1
=
n n
1
1
+
5n 5
2
Solve each problem.
31) 144 miles is what percent of 157.7 miles?
32) 30% of 148 m is what?
33) 90% of what is 45 tons?
34) What percent of 149 hours is 107 hours?
35) 53 ft is what percent of 84 ft?
36) 3% of what is 102 grams?
37) $92 is 45% of what?
38) 147 hours is 77% of what?
39) What is 31% of 24 inches?
40) $109 is 88% of what?
Simplify. Your answer should contain only positive exponents.
41)
43)
45)
(m 0n 3) 2
(m 3n 2) −3 ⋅ n 0
(2x −1) 2
−2 −4
−2 4
2x y
⋅x y
3 3
−2 3
x y ⋅ 2x y
( y −3 ⋅ x y −4) 4
42)
n
((2m ) ⋅ (m
4 2
−2 −4
44)
46)
x y
⋅y
))
−4
−2 −4 4
n
2
(2x 4 y 4) 4
( )
m
−1
−2
3 2
nn
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47)
49)
(2 yx −4) −2
3 2
4
4 2
( y 4) −4
−4 3
4
48)
50)
)
−1 4 3
0
2x y ⋅ 2 yx ⋅ x y
2x y ⋅ 2 yx
2u ⋅ (2u v
3 −1
2u v
(2x 2 y −3 ⋅ x 3 y 3) 2
2 −2
2x y
Write each number in scientific notation.
51) 0.2
52) 41000
53) 2.77
54) 0.000054
55) 163000
Write each number in standard notation.
56) 9.6 × 10
5
57) 1.3 × 10
58) 4.5 × 10
2
59) 4.49 × 10
60) 1.37 × 10
5
3
−1
Simplify. Write each answer in scientific notation.
61)
63)
65)
9 × 10
−6
2 × 10
−6
62)
8 × 10
4.1 × 10
0
9.2 × 10
4
2.7 × 10
4
8 × 10
3.7 × 10
64)
5 × 10
3
4
−1
4 × 10
1
4
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Find the slope of each line.
66)
67)
y
y
x
68)
x
69)
y
y
x
70)
x
y
x
Find the slope of the line through each pair of points.
71) (−13, 17), (−2, 12)
72) (19, −9), (−20, 6)
73) (−3, −6), (19, 12)
74) (−5, 11), (6, −6)
75) (4, −15), (17, −4)
Find the slope of each line.
76) 0 = x + 1 +
1
y
2
77) 9x − 20 = −5y
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78) 0 = −7x − 6 + 3 y
79) −8 + 3x = −4y
80) 0 = −x
Find the slope of a line parallel to each given line.
81) 4x = −50 − 10 y
Find the slope of a line perpendicular to each given line.
82) x = 10 − 5y
Sketch the graph of each line.
83) x − 2 y = −6
84) 5x − 2y = −2
y
y
6
6
5
5
4
4
3
3
2
2
1
1
−6 −5 −4 −3 −2 −1
1
−1
2
3
4
5
6 x
−6 −5 −4 −3 −2 −1
1
2
3
4
−1
−2
−2
−3
−3
−4
−4
−5
−5
−6
−6
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5
6 x
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85) 3x + y = 1
86) 4x + 3y = 15
y
y
6
6
5
5
4
4
3
3
2
2
1
1
−6 −5 −4 −3 −2 −1
1
2
3
4
5
−1
6 x
−6 −5 −4 −3 −2 −1
−2
−2
−3
−3
−4
−4
−5
−5
−6
−6
87) 7x − 5 y = 15
y
3
4
5
6 x
1
2
3
4
5
6 x
y
6
5
5
4
4
3
3
2
2
1
1
1
−1
2
88) x = 2
6
−6 −5 −4 −3 −2 −1
1
−1
2
3
4
5
6 x
−6 −5 −4 −3 −2 −1
−1
−2
−2
−3
−3
−4
−4
−5
−5
−6
−6
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89) 7x + 4 y = 12
90) 3x − 5y = −5
y
y
6
6
5
5
4
4
3
3
2
2
1
1
−6 −5 −4 −3 −2 −1
1
2
3
4
5
−1
6 x
−6 −5 −4 −3 −2 −1
−2
−2
−3
−3
−4
−4
−5
−5
−6
−6
91) x + 3 y = 9
1
2
3
4
5
6 x
1
2
3
4
5
6 x
−1
92) x = 1
y
y
6
6
5
5
4
4
3
3
2
2
1
1
−6 −5 −4 −3 −2 −1
1
−1
2
3
4
5
6 x
−6 −5 −4 −3 −2 −1
−1
−2
−2
−3
−3
−4
−4
−5
−5
−6
−6
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Write the slope-intercept form of the equation of each line.
93)
94)
y
y
4
4
2
2
−5 −4 −3 −2 −1
1
2
3
4
5 x
−5 −4 −3 −2 −1
−2
−2
−4
−4
1
2
3
4
5 x
Write the slope-intercept form of the equation of each line given the slope and y-intercept.
8
95) Slope = , y-intercept = 3
5
96) Slope = −2, y-intercept = 1
Write the slope-intercept form of the equation of each line.
97) 5x − 3 y = 18
99) y − 4 =
6
( x − 5)
5
98) y = −2
100) 0 = x + 2
Write the standard form of the equation of the line through the given point with the given slope.
101) through: (1, −2), slope = −4
102) through: (4, 2), slope =
5
4
Write the slope-intercept form of the equation of the line through the given point with the given
slope.
103) through: (3, 2), slope = −1
104) through: (−4, −3), slope =
1
2
Write the standard form of the equation of the line through the given points.
105) through: (1, 2) and (−5, 5)
106) through: (0, 2) and (1, −1)
Write the slope-intercept form of the equation of the line through the given points.
107) through: (3, −2) and (0, −5)
108) through: (0, 4) and (−1, 0)
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Write the standard form of the equation of the line described.
2
109) through: (3, −1), parallel to y = − x + 5
3
2
110) through: (2, −1), perp. to y = − x − 5
3
Solve each proportion.
111)
8 n+3
=
3 7n + 7
112)
2m − 4 7m − 7
=
10
9
113)
6
2
=−
r+6
r−2
114)
n − 1 n + 10
=
7
8
115)
v+2
7
=−
2v − 9
2
Find each percent change. State if it is an increase or a decrease.
116) From 48 to 33
117) From 70 to 22
118) From 21 to 10
119) From 50 to 43
120) From 30 to 29
Sketch the graph of each linear inequality.
121) 2x + 3 y ≤ 15
122) 3x + y > −5
y
y
6
6
5
5
4
4
3
3
2
2
1
1
−6 −5 −4 −3 −2 −1
1
−1
2
3
4
5
6 x
−6 −5 −4 −3 −2 −1
1
2
3
−1
−2
−2
−3
−3
−4
−4
−5
−5
−6
−6
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4
5
6 x
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123) 7x + 5 y ≥ 25
124) 5x + 2y ≥ −8
y
y
6
6
5
5
4
4
3
3
2
2
1
1
−6 −5 −4 −3 −2 −1
1
2
3
4
5
−1
6 x
−6 −5 −4 −3 −2 −1
1
2
3
4
5
−1
−2
−2
−3
−3
−4
−4
−5
−5
−6
−6
6 x
125) x − 2 y ≥ −2
y
6
5
4
3
2
1
−6 −5 −4 −3 −2 −1
1
−1
2
3
4
5
6 x
−2
−3
−4
−5
−6
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Graph each equation.
126) y = − x + 4
127) y = − x − 4
y
y
6
6
5
5
4
4
3
3
2
2
1
1
−6 −5 −4 −3 −2 −1
1
−1
2
3
4
5
6 x
−6 −5 −4 −3 −2 −1
1
2
3
4
−1
−2
−2
−3
−3
−4
−4
−5
−5
−6
−6
5
6 x
Solve each system of equations for x and y
128) −9 y = −3x − 45
−3 y = 9 − 5x
129) −45 − 8x = 5y
5y = 4x + 15
130) 45 + 5 y = −16x
5 y + 16x = −45
131) −3 + 4x − 3y = 0
x = −15 + 3y
132) 2 y + 10 + x = 0
0 = −2y + x + 2
133) 8y = −8 − 14x
x = −4 y − 28
134) −2 = − y + x
4x = 27 − 3y
135) −42 − 3x − 7y = 0
−5 + y + 2x = 0
136) − y = −6 + 3x
3 y + 9x − 18 = 0
137) 3y = −x − 6
−18y = −162 + 28x
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Sketch the solution to each system of inequalities.
138) 2x − y ≤ 1
2x − y ≤ −1
139) 4x − y ≥ −1
x− y<2
y
−5
−4
−3
−2
y
5
5
4
4
3
3
2
2
1
1
−1
1
2
3
4
5 x
−5
−4
−3
−2
−1
−1
−1
−2
−2
−3
−3
−4
−4
−5
−5
140) x + 3 y ≥ 6
2x + y ≥ −3
141) x − 3y > 3
x + 3y > −9
y
−5
−4
−3
−2
2
3
4
5 x
1
2
3
4
5 x
y
5
5
4
4
3
3
2
2
1
1
−1
1
1
2
3
4
5 x
−5
−4
−3
−2
−1
−1
−1
−2
−2
−3
−3
−4
−4
−5
−5
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142) 2x − y ≥ 3
y < −1
y
5
4
3
2
1
−5
−4
−3
−2
−1
1
2
3
4
5 x
−1
−2
−3
−4
−5
Solve each equation.
143) m = 4
145)
n
=2
6
147)
n
=5
2
144) a = 8
146) b + 4 = 1
148)
x
=4
2
149) −2 + 4x = 26
150) 4 − 5a = 14
151) 3v − 3 = 3
152) 3 + 6x = 15
153) −2 5x + 4 = −38
154) 4 − p + 3 = 5
155) −3 −2v − 6 = −12
156) −7 + 7b − 3 = 25
157) −7 −2 − 3b = −35
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Draw a graph for each inequality.
158) 3 ≥ x
159) −n > −4
−7 −6 −5 −4 −3 −2 −1 0
1
2
3
4
5
6
7
1
2
3
4
5
6
7
−7 −6 −5 −4 −3 −2 −1 0
1
2
3
4
5
6
7
−7 −6 −5 −4 −3 −2 −1 0
1
2
3
4
5
2
3
160) 3 ≤ −a
−7 −6 −5 −4 −3 −2 −1 0
Write an inequality for each graph.
161)
162)
−7 −6 −5 −4 −3 −2 −1 0
1
2
3
4
5
6
7
−7 −6 −5 −4 −3 −2 −1 0
1
2
3
4
5
6
7
6
7
163)
Solve each inequality and graph its solution.
n
<1
10
164)
−12
−8
166)
165) −5 + b > −17
−7 −6 −5 −4 −3 −2 −1
−4
0
4
8
−8
−6
0
1
2
3
4
5
6
6
169) b − 4 < −16
−6 −5 −4 −3 −2 −1
−4
−2
0
2
4
6
1
2
3
4
5
6
6
8
5
6
8
1
2
3
4
5
172) 6n > 60
−4
0
171) 2 + p > 6
−9 −8 −7 −6 −5 −4 −3 −2 −1 0
−8
5
−8 −7 −6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6 7 8
7
170) 2 + x ≥ 3
−12
4
167) 5x ≤ 30
r
>2
3
168)
1
12
p − 4 > −2
−6 −5 −4 −3 −2 −1
0
6
−12 −10 −8
−6
−4
−2
0
2
4
173) n + 1 > −1
0
4
8
−6 −5 −4 −3 −2 −1
12
0
1
2
3
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Simplify.
174) −2 3 + 2 5 + 2 12
175) − 18 + 3 2 −
176) − 3 − 2 27 + 3 18
177) 2 6 −
178) −2 24 + 2 20 − 2 6
179) − 3 (2 +
180) −3 6 (4 − 5 6 )
181)
3 ( 6 + 2)
183)
5 (4 − 4 2 )
5 (−4 5 + 3)
182)
184) (3 +
3 )(5 +
3)
186)
(
3 − 4 2 )( 3 − 2 2 )
188)
(
2+
3)
5 − 3 24
6)
185) (3 + 5 5 )(−3 − 3 5 )
187)
(
3+
2
5 )(−4 3 + 3 3 )
5
189)
2 5−
3
190)
194)
3
5−
3 5+
3+
3
193)
4−
196)
2+5 5
5
2+
2
2
191)
2−3
192)
8
2
195)
2
2
−2 + 4 5
2−4 3
2
2−4 5
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Solve each equation. Remember to check for extraneous solutions.
197) 2 =
p
198) 1 =
199) 1 =
n
5
200)
x
=2
2
202)
3n − 4 =
204)
4x =
201)
12 − 2 p =
203)
p
=
2
205) r =
207)
7− p
6− p
20 − r
5x = x
209) r − 2 =
2r − 1
b
6 − 2x
206) b =
2b
208) a =
20 − a
210) −1 =
2n − 2
n−1−n
Solve each equation by factoring.
211) (2v − 1)(v − 4) = 0
212) (3n + 2)(n − 4) = 0
213) (2n − 1)(n − 5) = 0
214) (5k + 2)(k − 2) = 0
215) (2x + 3)(5x + 4) = 0
216) x 2 − 15x = −56
217) n 2 − 32 = −4n
218) x 2 = −8x
219) x 2 − 25 = 0
220) 5v 2 − 15v = −10
221) −32 + 40v = −12v 2
222) 2m 2 − 13m + 22 = 1
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Worksheet by Kuta Software LLC
223) 4n 2 − 2 = −n 2 − 8 − 13n
224) 345k 2 + 196k + 34 = 6 + 2k 2
225) 3m 2 + 11m = −2m − 12
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Worksheet by Kuta Software LLC
Algebra 1
Name___________________________________ ID: 1
Assignment
Date________________ Period____
Simplify each expression.
1) −
32x 5
16x 4
2)
−2x
3)
48n 2
32n 4
3
2n 2
5) −
7)
9)
11)
4)
18v 2
12v 3
3
−
2v
6)
5x 2 + 8x − 21
3x 2 + 9x
5x − 7
3x
8)
20k 2 + 4k
28k 2 − 8k
5k + 1
7k − 2
10)
n − 5 15n 2 − 36n − 27
⋅
5n + 3
3n − 9
n−5
13) (2n 2 − 19n + 42) ⋅
7n + 1
14n − 47n − 7
2
12)
90n 3
40n 2
9n
4
10x
20x 2
1
2x
5x 2 + 3x − 8
8x 2 − 8x
5x + 8
8x
12m + 28
12m + 12
3m + 7
3(m + 1)
5a 2 + 28a − 12
4a + 24
5a − 2
4
18r + 45
1
9
⋅
8
2r + 5 8
14) (2m − 9) ⋅
m+6
m+6
2m − 13m + 18 m − 2
2
n−6
15)
5v 2 − 8v − 21
1
v−3
⋅
5v + 7
v−8 v−8
16)
17)
8
1
8(n − 5)
÷ 2
2
15n − 12n 5n − 29n + 20
3n
18)
19)
m+2
m−5
m+2
÷
18m + 45 18m + 45 m − 5
20)
27 p − 9
9
÷
3p − 1
p−2
p−2
7n 2 − 7
1
÷
2
21n + 28n − 49 3n + 7
n+1
18a − 81
1
÷
2
14a − 79a + 72 7a − 8
9
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Worksheet by Kuta Software LLC
Solve each equation. Remember to check for extraneous solutions.
1
1
1
+
=
4 4n 2n
{1}
22) 1 =
23)
2 5
= +1
a a
{−3}
24)
6
1
=1−
b
b
{7}
26)
5
1
=1−
4m
4m
28)
1
1
1
− =
5x
2 10x
30)
5
4
1
= 2
+
n − 5n n − 5n n
{6}
25)
27)
1
n−2 1
−
= 2
2
4n
2n 2
n
{}
1
2
m−1
1
=1+
3m
3m
{−1}
29) 1 +
6 1
=
n n
{−5}
1
1
+
5n 5
{}
21)
1
4
{}
3
2
{}
1
5
2
Solve each problem.
31) 144 miles is what percent of 157.7 miles?
91.3%
32) 30% of 148 m is what?
44.4 m
33) 90% of what is 45 tons?
50 tons
34) What percent of 149 hours is 107 hours?
71.8%
35) 53 ft is what percent of 84 ft?
63.1%
36) 3% of what is 102 grams?
3400 grams
37) $92 is 45% of what?
$204.44
38) 147 hours is 77% of what?
190.9 hours
39) What is 31% of 24 inches?
7.4 inches
40) $109 is 88% of what?
$123.86
Simplify. Your answer should contain only positive exponents.
41)
(m 0n 3) 2
(m 3n 2) −3 ⋅ n 0
42)
n
((2m ) ⋅ (m
4 2
))
−4
−2 −4 4
n
256
n 63
m 9 n 12
43)
45)
(2x −1) 2
−2 −4
−2 −4
44)
−2 4
2x y
2x 2
⋅x y
3 3
−2 3
x y ⋅ 2x y
( y −3 ⋅ x y −4) 4
2y 34
x3
46)
x y
⋅y
(2x y )
4 4 4
( )
m
−1
2
1
16x 18 y 18
−2
3 2
nn
m 2 n 10
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Worksheet by Kuta Software LLC
47)
49)
(2 yx −4) −2
3 2
4
4 2
2x y ⋅ 2 yx ⋅ x y
( y 4) −4
−4 3
2x y ⋅ 2 yx
4
1
16y 7 x 3
1
4y 20
2u ⋅ (2u v
48)
50)
)
−1 4 3
0
3 −1
2u v
8v 13
u6
(2x 2 y −3 ⋅ x 3 y 3) 2
2 −2
2x y
2 8
2y x
Write each number in scientific notation.
51) 0.2
52) 41000
2 × 10
−1
4.1 × 10
53) 2.77
4
54) 0.000054
2.77 × 10
0
5.4 × 10
−5
55) 163000
1.63 × 10
5
Write each number in standard notation.
56) 9.6 × 10
960000
5
57) 1.3 × 10
130000
58) 4.5 × 10
450
2
59) 4.49 × 10
4490
60) 1.37 × 10
0.137
5
3
−1
Simplify. Write each answer in scientific notation.
61)
9 × 10
−6
2 × 10
−6
62)
8 × 10
4
4.625 × 10
4.1 × 10
0
5 × 10
9.2 × 10
4
4.457 × 10
65)
3
0
4.5 × 10
63)
3.7 × 10
2.7 × 10
8 × 10
64)
−1
4 × 10
−5
−2
1
1.25 × 10
−2
4
4
3.375 × 10
−1
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Worksheet by Kuta Software LLC
Find the slope of each line.
66)
67)
y
y
x
x
1
68)
−1
69)
y
y
x
x
Undefined
70)
−2
5
2
y
x
Find the slope of the line through each pair of points.
5
5
71) (−13, 17), (−2, 12) −
72) (19, −9), (−20, 6) −
11
13
73) (−3, −6), (19, 12)
9
11
75) (4, −15), (17, −4)
11
13
74) (−5, 11), (6, −6) −
17
11
Find the slope of each line.
1
76) 0 = x + 1 + y
2
−2
77) 9x − 20 = −5y −
9
5
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Worksheet by Kuta Software LLC
7
3
78) 0 = −7x − 6 + 3 y
79) −8 + 3x = −4y −
3
4
80) 0 = −x
Undefined
Find the slope of a line parallel to each given line.
2
81) 4x = −50 − 10 y −
5
Find the slope of a line perpendicular to each given line.
82) x = 10 − 5y
5
Sketch the graph of each line.
83) x − 2 y = −6
84) 5x − 2y = −2
y
y
6
6
5
5
4
4
3
3
2
2
1
1
−6 −5 −4 −3 −2 −1
1
−1
2
3
4
5
6 x
−6 −5 −4 −3 −2 −1
1
2
3
4
5
−1
−2
−2
−3
−3
−4
−4
−5
−5
−6
−6
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6 x
Worksheet by Kuta Software LLC
85) 3x + y = 1
86) 4x + 3y = 15
y
y
6
6
5
5
4
4
3
3
2
2
1
1
−6 −5 −4 −3 −2 −1
1
2
3
4
5
−1
6 x
−6 −5 −4 −3 −2 −1
−2
−2
−3
−3
−4
−4
−5
−5
−6
−6
87) 7x − 5 y = 15
y
3
4
5
6 x
1
2
3
4
5
6 x
y
6
5
5
4
4
3
3
2
2
1
1
1
−1
2
88) x = 2
6
−6 −5 −4 −3 −2 −1
1
−1
2
3
4
5
6 x
−6 −5 −4 −3 −2 −1
−1
−2
−2
−3
−3
−4
−4
−5
−5
−6
−6
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Worksheet by Kuta Software LLC
89) 7x + 4 y = 12
90) 3x − 5y = −5
y
y
6
6
5
5
4
4
3
3
2
2
1
1
−6 −5 −4 −3 −2 −1
1
2
3
4
5
−1
6 x
−6 −5 −4 −3 −2 −1
−2
−2
−3
−3
−4
−4
−5
−5
−6
−6
91) x + 3 y = 9
1
2
3
4
5
6 x
1
2
3
4
5
6 x
−1
92) x = 1
y
y
6
6
5
5
4
4
3
3
2
2
1
1
−6 −5 −4 −3 −2 −1
1
−1
2
3
4
5
6 x
−6 −5 −4 −3 −2 −1
−1
−2
−2
−3
−3
−4
−4
−5
−5
−6
−6
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Worksheet by Kuta Software LLC
Write the slope-intercept form of the equation of each line.
93)
94)
y
y
4
4
2
2
−5 −4 −3 −2 −1
1
2
3
4
5 x
3
y=− x−2
5
−5 −4 −3 −2 −1
−2
−2
−4
−4
1
2
3
4
5 x
y = 5x + 1
Write the slope-intercept form of the equation of each line given the slope and y-intercept.
8
8
95) Slope = , y-intercept = 3 y = x + 3
5
5
96) Slope = −2, y-intercept = 1
y = −2x + 1
Write the slope-intercept form of the equation of each line.
5
97) 5x − 3 y = 18 y = x − 6
98) y = −2
3
y = −2
99) y − 4 =
6
( x − 5) y = 6 x − 2
5
5
100) 0 = x + 2
x = −2
Write the standard form of the equation of the line through the given point with the given slope.
101) through: (1, −2), slope = −4
4x + y = 2
102) through: (4, 2), slope =
5
4
5x − 4 y = 12
Write the slope-intercept form of the equation of the line through the given point with the given
slope.
103) through: (3, 2), slope = −1
y = −x + 5
104) through: (−4, −3), slope =
1
1
y= x−1
2
2
Write the standard form of the equation of the line through the given points.
105) through: (1, 2) and (−5, 5)
x + 2y = 5
106) through: (0, 2) and (1, −1)
3x + y = 2
Write the slope-intercept form of the equation of the line through the given points.
107) through: (3, −2) and (0, −5)
y=x−5
108) through: (0, 4) and (−1, 0)
y = 4x + 4
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Worksheet by Kuta Software LLC
Write the standard form of the equation of the line described.
2
109) through: (3, −1), parallel to y = − x + 5
3
2x + 3 y = 3
2
110) through: (2, −1), perp. to y = − x − 5
3
3x − 2 y = 8
Solve each proportion.
111)
113)
115)
8 n+3
=
3 7n + 7
{−0.88}
112)
6
2
=−
r+6
r−2
{0}
114)
2m − 4 7m − 7
=
10
9
{0.65}
n − 1 n + 10
=
7
8
{78}
v+2
7
=−
2v − 9
2
{3.68}
Find each percent change. State if it is an increase or a decrease.
116) From 48 to 33
31.3% decrease
117) From 70 to 22
68.6% decrease
118) From 21 to 10
52.4% decrease
119) From 50 to 43
14% decrease
120) From 30 to 29
3.3% decrease
Sketch the graph of each linear inequality.
121) 2x + 3 y ≤ 15
122) 3x + y > −5
y
y
6
6
5
5
4
4
3
3
2
2
1
1
−6 −5 −4 −3 −2 −1
1
−1
2
3
4
5
6 x
−6 −5 −4 −3 −2 −1
1
2
3
−1
−2
−2
−3
−3
−4
−4
−5
−5
−6
−6
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4
5
6 x
Worksheet by Kuta Software LLC
123) 7x + 5 y ≥ 25
124) 5x + 2y ≥ −8
y
y
6
6
5
5
4
4
3
3
2
2
1
1
−6 −5 −4 −3 −2 −1
1
2
3
4
5
−1
6 x
−6 −5 −4 −3 −2 −1
1
2
3
−1
−2
−2
−3
−3
−4
−4
−5
−5
−6
−6
4
5
6 x
125) x − 2 y ≥ −2
y
6
5
4
3
2
1
−6 −5 −4 −3 −2 −1
1
−1
2
3
4
5
6 x
−2
−3
−4
−5
−6
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Worksheet by Kuta Software LLC
Graph each equation.
126) y = − x + 4
127) y = − x − 4
y
y
6
6
5
5
4
4
3
3
2
2
1
1
−6 −5 −4 −3 −2 −1
1
−1
2
3
4
5
6 x
−6 −5 −4 −3 −2 −1
1
2
3
4
−1
−2
−2
−3
−3
−4
−4
−5
−5
−6
−6
5
6 x
Solve each system of equations for x and y
128) −9 y = −3x − 45
−3 y = 9 − 5x
(6, 7)
129) −45 − 8x = 5y
5y = 4x + 15
(−5, −1)
130) 45 + 5 y = −16x
5 y + 16x = −45
Infinite number of solutions
131) −3 + 4x − 3y = 0
x = −15 + 3y
(6, 7)
132) 2 y + 10 + x = 0
0 = −2y + x + 2
(−6, −2)
133) 8y = −8 − 14x
x = −4 y − 28
(4, −8)
134) −2 = − y + x
4x = 27 − 3y
(3, 5)
135) −42 − 3x − 7y = 0
−5 + y + 2x = 0
(7, −9)
136) − y = −6 + 3x
3 y + 9x − 18 = 0
Infinite number of solutions
137) 3y = −x − 6
−18y = −162 + 28x
(9, −5)
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Worksheet by Kuta Software LLC
Sketch the solution to each system of inequalities.
138) 2x − y ≤ 1
2x − y ≤ −1
139) 4x − y ≥ −1
x− y<2
y
−5
−4
−3
−2
y
5
5
4
4
3
3
2
2
1
1
−1
1
2
3
4
5 x
−5
−4
−3
−2
−1
−1
−1
−2
−2
−3
−3
−4
−4
−5
−5
140) x + 3 y ≥ 6
2x + y ≥ −3
141) x − 3y > 3
x + 3y > −9
y
−5
−4
−3
−2
2
3
4
5 x
1
2
3
4
5 x
y
5
5
4
4
3
3
2
2
1
1
−1
1
1
2
3
4
5 x
−5
−4
−3
−2
−1
−1
−1
−2
−2
−3
−3
−4
−4
−5
−5
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Worksheet by Kuta Software LLC
142) 2x − y ≥ 3
y < −1
y
5
4
3
2
1
−5
−4
−3
−2
−1
1
2
3
4
5 x
−1
−2
−3
−4
−5
Solve each equation.
143) m = 4
144) a = 8
{4, −4}
145)
{8, −8}
n
=2
6
146) b + 4 = 1
{−3, −5}
{12, −12}
147)
n
=5
2
148)
{10, −10}
x
=4
2
{8, −8}
149) −2 + 4x = 26
{7, −6}
151) 3v − 3 = 3
{2, 0}
18
5
152) 3 + 6x = 15
{
153) −2 5x + 4 = −38 3, −
23
5
}
155) −3 −2v − 6 = −12
{−5, −1}
{ }
150) 4 − 5a = 14 −2,
{2, −3}
154) 4 − p + 3 = 5
{2, 6}
156) −7 + 7b − 3 = 25
{5, −3}
{ }
7
157) −7 −2 − 3b = −35 − , 1
3
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Worksheet by Kuta Software LLC
Draw a graph for each inequality.
158) 3 ≥ x
159) −n > −4
−7 −6 −5 −4 −3 −2 −1 0
1
2
3
4
5
6
7
1
2
3
4
5
6
7
−7 −6 −5 −4 −3 −2 −1 0
1
2
3
4
5
6
7
−7 −6 −5 −4 −3 −2 −1 0
1
2
3
4
5
2
3
160) 3 ≤ −a
−7 −6 −5 −4 −3 −2 −1 0
Write an inequality for each graph.
161)
162)
−7 −6 −5 −4 −3 −2 −1 0
1
2
3
4
5
6
7
b≤6
6
7
m≥5
163)
−7 −6 −5 −4 −3 −2 −1 0
1
2
3
4
5
6
7
k≥3
Solve each inequality and graph its solution.
n
<1
10
164)
−12
−8
165) −5 + b > −17
−7 −6 −5 −4 −3 −2 −1
−4
0
4
8
0
1
4
5
6
{ All real numbers. }
12
−10 < n < 10
166)
p − 4 > −2
−6 −5 −4 −3 −2 −1
167) 5x ≤ 30
0
1
2
3
4
5
6
{ All real numbers. }
−6 ≤ x ≤ 6
r
>2
3
168)
−8
−6
−8 −7 −6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6 7 8
7
169) b − 4 < −16
−6 −5 −4 −3 −2 −1
−4
−2
0
2
4
6
0
1
2
3
4
5
6
6
8
5
6
No solution.
8
r > 6 or r < −6
170) 2 + x ≥ 3
171) 2 + p > 6
−9 −8 −7 −6 −5 −4 −3 −2 −1 0
1
2
3
4
5
x ≥ 1 or x ≤ −5
−8
−12 −10 −8
−6
−4
−2
0
2
4
p > 4 or p < −8
172) 6n > 60
−12
6
−4
n > 10 or n < −10
173) n + 1 > −1
0
4
8
−6 −5 −4 −3 −2 −1
12
0
1
2
3
4
{ All real numbers. }
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Worksheet by Kuta Software LLC
Simplify.
174) −2 3 + 2 5 + 2 12
175) − 18 + 3 2 −
2 3+2 5
−2 2
176) − 3 − 2 27 + 3 18
177) 2 6 −
−7 3 + 9 2
−4 6 −
178) −2 24 + 2 20 − 2 6
3 2+2 3
5 (−4 5 + 3)
4 5 − 4 10
3 )(5 +
3)
185) (3 + 5 5 )(−3 − 3 5 )
18 + 8 3
−84 − 24 5
3 − 4 2 )( 3 − 2 2 )
187)
19 − 6 6
188)
(
5
189)
3
191)
5
193)
2+
15
2 5−
−3 2 − 9
7
2−3
192)
5 )(−4 3 + 3 3 )
3+
2
5+2 6
190)
(
−3 −
3)
2+
5 (4 − 4 2 )
183)
−20 + 3 5
(
6)
3 ( 6 + 2)
181)
−12 6 + 90
186)
5
−2 3 − 3 2
180) −3 6 (4 − 5 6 )
184) (3 +
5 − 3 24
179) − 3 (2 +
−6 6 + 4 5
182)
8
3
10 + 10
18
2
2
−4 + 10 5
121
2+5 5
3
5−
15 + 3 2
23
2
10 − 5 3
194)
3 5+
4−
196)
3+
2 12 5 + 3 10 + 4 2 + 2
14
2
195)
−2 + 4 5 1 + 2 3 − 2 5 − 4 15
11
2−4 3
2
−3 − 6 5 − 2 − 2 10
38
2−4 5
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Worksheet by Kuta Software LLC
Solve each equation. Remember to check for extraneous solutions.
197) 2 =
{4}
p
198) 1 =
{1}
n
5
199) 1 =
201)
{8}
12 − 2 p =
7− p
202)
{5}
3n − 4 =
2n − 2
{2}
p
=
2
203)
x
=2
2
200)
{5}
b
6− p
204)
4x =
6 − 2x
{1}
{4}
205) r =
{4}
207)
20 − r
5x = x
{0, 5}
209) r − 2 =
{5}
206) b = 2b
{0, 2}
208) a =
{4}
2r − 1
20 − a
210) −1 =
{2, 1}
n−1−n
Solve each equation by factoring.
211) (2v − 1)(v − 4) = 0
1
,4
2
212) (3n + 2)(n − 4) = 0
2
− ,4
3
213) (2n − 1)(n − 5) = 0
1
,5
2
214) (5k + 2)(k − 2) = 0
2
− ,2
5
215) (2x + 3)(5x + 4) = 0
3 4
− ,−
2 5
216) x 2 − 15x = −56
217) n 2 − 32 = −4n
218) x 2 = −8x
{ }
{ }
{
{ }
{ }
}
{8, 7}
{−8, 4}
219) x 2 − 25 = 0
{−8, 0}
220) 5v 2 − 15v = −10
{5, −5}
221) −32 + 40v = −12v 2
2
, −4
3
{ }
{2, 1}
222) 2m 2 − 13m + 22 = 1
7
,3
2
{ }
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Worksheet by Kuta Software LLC
223) 4n 2 − 2 = −n 2 − 8 − 13n
3
− , −2
5
{
}
224) 345k 2 + 196k + 34 = 6 + 2k 2
2
−
7
{ }
225) 3m 2 + 11m = −2m − 12
4
− , −3
3
{
}
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Worksheet by Kuta Software LLC