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Math Problems
Algebra 1
Solve linear equations: mixed review
48
/
4
×
v
for
v
=
4
48 / 4 \times v \text{ for } v = 4
48/4
×
v
for
v
=
4
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2
x
+
17
−
5
x
−
20
=
53
2x+17-5x-20=53
2
x
+
17
−
5
x
−
20
=
53
solve for
x
x
x
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2
x
+
3
y
=
5
x
−
y
2x+3y=5x-y
2
x
+
3
y
=
5
x
−
y
missing value of
x
x
x
when
y
y
y
is
0
0
0
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−
3
-3
−
3
x
x
x
+
3
3
3
y
y
y
=
4
4
4
-
x
x
x
+
y
y
y
=
3
3
3
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13
+
4
x
=
2
(
11
x
+
20
)
+
x
13 + 4x = 2(11x + 20) + x
13
+
4
x
=
2
(
11
x
+
20
)
+
x
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if
n
+
57
=
95
n + 57 = 95
n
+
57
=
95
and
n
+
32
−
z
=
43
n + 32 - z = 43
n
+
32
−
z
=
43
then what is
z
z
z
?
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Solve for
j
j
j
.
\newline
j
4
−
−
14
=
17
\frac{j}{4}--14=17
4
j
−
−
14
=
17
\newline
j
=
j=
j
=
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25
y
−
30
=
4
y
−
28
25y-30=4y-28
25
y
−
30
=
4
y
−
28
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Lesson
10
10
10
Practice Problems
\newline
1
1
1
. a. Explain how we know that triangle
A
B
C
A B C
A
BC
and triangle
D
E
F
D E F
D
EF
are similar.
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8
8
8
−
33
-33
−
33
Soive each equation below for
x
x
x
. Check each solution.
\newline
a.
2
x
−
10
=
0
2 x-10=0
2
x
−
10
=
0
\newline
b.
x
+
6
=
0
x+6=0
x
+
6
=
0
\newline
c.
(
2
x
−
10
)
(
x
+
6
)
=
0
(2 x-10)(x+6)=0
(
2
x
−
10
)
(
x
+
6
)
=
0
\newline
d.
4
x
+
1
=
0
4 x+1=0
4
x
+
1
=
0
\newline
e.
x
−
8
=
0
x-8=0
x
−
8
=
0
\newline
f.
(
4
x
+
1
)
(
x
−
8
)
=
0
(4 x+1)(x-8)=0
(
4
x
+
1
)
(
x
−
8
)
=
0
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Solving equations
\newline
1
1
1
) Solve for
B
B
B
in the following
\newline
a)
B
=
4
(
3
)
+
10
B=4(3)+10
B
=
4
(
3
)
+
10
\newline
b)
B
=
−
18
+
2.5
(
10
)
B=-18+2.5(10)
B
=
−
18
+
2.5
(
10
)
\newline
2
2
2
) Solve for
N
\mathrm{N}
N
in the following
\newline
a)
85
=
20
+
5
N
85=20+5 \mathrm{~N}
85
=
20
+
5
N
\newline
b)
20
=
268
−
8
N
20=268-8 \mathrm{~N}
20
=
268
−
8
N
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Solve for the exact value of
x
x
x
.
\newline
3
ln
(
7
x
−
6
)
+
19
=
31
3 \ln (7 x-6)+19=31
3
ln
(
7
x
−
6
)
+
19
=
31
\newline
Answer:
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Solve for the exact value of
x
x
x
.
\newline
6
ln
(
3
x
+
2
)
+
20
=
56
6 \ln (3 x+2)+20=56
6
ln
(
3
x
+
2
)
+
20
=
56
\newline
Answer:
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Solve for the exact value of
x
x
x
.
\newline
4
ln
(
7
x
+
3
)
+
19
=
43
4 \ln (7 x+3)+19=43
4
ln
(
7
x
+
3
)
+
19
=
43
\newline
Answer:
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Solve for the exact value of
x
x
x
.
\newline
3
ln
(
2
x
+
7
)
+
14
=
20
3 \ln (2 x+7)+14=20
3
ln
(
2
x
+
7
)
+
14
=
20
\newline
Answer:
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12
=
n
−
9
12 = n - 9
12
=
n
−
9
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Evaluate
9
150
300
\frac{9^{150}}{300}
300
9
150
\newline
A)
18
18
18
\newline
B)
9
9
9
\newline
C)
3
3
3
\newline
D)
81
81
81
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Example
1
1
1
: Solve for
x
:
2
(
3
x
+
1
)
x: 2(3 x+1)
x
:
2
(
3
x
+
1
)
\newline
+
3
(
5
x
+
2
)
=
x
−
1
+3(5 x+2)=x-1
+
3
(
5
x
+
2
)
=
x
−
1
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solution of substitution
y
=
4
x
−
45
y= 4x - 45
y
=
4
x
−
45
!&
6
x
+
2
y
=
78
6x + 2y =78
6
x
+
2
y
=
78
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6
+
8
a
+
12
=
5
a
+
15
b
+
6
+
8
a
+
12
6+8 a+12=5 a+15 b+6+8 a+12
6
+
8
a
+
12
=
5
a
+
15
b
+
6
+
8
a
+
12
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solve for
x
x
x
,
\newline
x
+
10
x
−
10
=
0
x + 10x -10=0
x
+
10
x
−
10
=
0
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Solve for
u
u
u
.
\newline
u
4
+
4
=
8
\frac{u}{4} + 4 = 8
4
u
+
4
=
8
\newline
u
=
u =
u
=
_
_
_
_
_
\_\_\_\_\_
_____
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Solve for
m
m
m
.
\newline
m
3
+
7
=
11
\frac{m}{3} + 7 = 11
3
m
+
7
=
11
\newline
m
=
m =
m
=
_
_
_
_
_
\_\_\_\_\_
_____
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Solve for
j
j
j
.
\newline
j
+
9
4
=
4
j + \frac{9}{4} = 4
j
+
4
9
=
4
\newline
j
=
_
_
_
_
j = \_\_\_\_
j
=
____
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Solve for
c
c
c
.
\newline
c
3
+
14
=
18
\frac{c}{3} + 14 = 18
3
c
+
14
=
18
\newline
c
=
c =
c
=
_
_
_
_
_
\_\_\_\_\_
_____
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Solve for
k
k
k
.
\newline
2
=
k
4
−
2
2 = \frac{k}{4} - 2
2
=
4
k
−
2
\newline
k
=
k =
k
=
_
_
_
_
_
\_\_\_\_\_
_____
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Solve for
n
n
n
.
\newline
n
4
−
2
=
2
\frac{n}{4} - 2 = 2
4
n
−
2
=
2
\newline
n
=
n =
n
=
_
_
_
_
_
\_\_\_\_\_
_____
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Solve for
v
v
v
.
\newline
v
2
+
12
=
15
\frac{v}{2} + 12 = 15
2
v
+
12
=
15
\newline
v
=
v =
v
=
_____
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Solve for
c
c
c
.
\newline
c
2
−
2
=
1
\frac{c}{2} - 2 = 1
2
c
−
2
=
1
\newline
c
=
c =
c
=
_____
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Solve for
d
d
d
.
\newline
d
3
−
1
=
1
\frac{d}{3} - 1 = 1
3
d
−
1
=
1
\newline
d
=
d =
d
=
_
_
_
_
_
\_\_\_\_\_
_____
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Solve for
h
h
h
.
\newline
h
4
−
2
=
2
\frac{h}{4} - 2 = 2
4
h
−
2
=
2
\newline
h
=
h =
h
=
_
_
_
_
_
\_\_\_\_\_
_____
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Solve for
w
w
w
.
\newline
w
4
+
9
=
11
\frac{w}{4} + 9 = 11
4
w
+
9
=
11
\newline
w
=
w =
w
=
_
_
_
_
_
\_\_\_\_\_
_____
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Solve for
n
n
n
.
\newline
n
4
+
5
=
9
\frac{n}{4} + 5 = 9
4
n
+
5
=
9
\newline
n
=
n =
n
=
_
_
_
_
_
\_\_\_\_\_
_____
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Solve for
n
n
n
.
\newline
n
4
−
2
=
1
\frac{n}{4} - 2 = 1
4
n
−
2
=
1
\newline
n
=
n =
n
=
_____
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Solve for
q
q
q
.
\newline
15
+
1
−
12
q
=
−
18
q
−
14
15 + 1 - 12q = -18q - 14
15
+
1
−
12
q
=
−
18
q
−
14
\newline
q
=
q =
q
=
__
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Solve for
y
y
y
.
\newline
2
−
1
8
y
=
11
+
7
8
y
2 - \frac{1}{8}y = 11 + \frac{7}{8}y
2
−
8
1
y
=
11
+
8
7
y
\newline
y
=
y =
y
=
____
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Solve for
w
w
w
.
\newline
2
w
+
18
=
12
2w + 18 = 12
2
w
+
18
=
12
\newline
w
=
w =
w
=
____
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Solve for
q
q
q
.
\newline
9
q
−
8
q
+
q
=
14
9q - 8q + q = 14
9
q
−
8
q
+
q
=
14
\newline
q
=
q =
q
=
____
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Solve for
j
j
j
.
\newline
−
4
j
=
2
3
j
+
2
−
4
j
-4j = \frac{2}{3}j + 2 - 4j
−
4
j
=
3
2
j
+
2
−
4
j
\newline
j
=
j =
j
=
____
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Solve for
g
g
g
.
\newline
5
3
g
=
2
g
−
2
3
g
+
2
\frac{5}{3}g = 2g - \frac{2}{3}g + 2
3
5
g
=
2
g
−
3
2
g
+
2
\newline
g
=
_
_
_
g = \_\_\_
g
=
___
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Solve for
m
m
m
.
\newline
m
−
−
12
−
4
=
−
4
m - \frac{-12}{-4} = -4
m
−
−
4
−
12
=
−
4
\newline
m
=
m =
m
=
_____
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Solve for
b
b
b
.
\newline
−
b
+
10
b
+
2
b
+
17
=
6
-b + 10b + 2b + 17 = 6
−
b
+
10
b
+
2
b
+
17
=
6
\newline
b
=
b =
b
=
__
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Solve for
h
h
h
.
\newline
6
−
h
=
1
6 - h = 1
6
−
h
=
1
\newline
h
=
h =
h
=
_
_
_
_
_
\_\_\_\_\_
_____
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Solve for
v
v
v
.
\newline
−
6
v
−
20
−
17
v
=
19
−
20
v
-6v - 20 - 17v = 19 - 20v
−
6
v
−
20
−
17
v
=
19
−
20
v
\newline
v
=
v =
v
=
____
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Solve for
s
s
s
.
\newline
−
20
+
12
s
−
15
=
20
+
7
s
-20 + 12s - 15 = 20 + 7s
−
20
+
12
s
−
15
=
20
+
7
s
\newline
s
=
s =
s
=
__
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Solve for
h
h
h
.
\newline
−
15
h
−
17
+
14
=
15
−
13
h
-15h - 17 + 14 = 15 - 13h
−
15
h
−
17
+
14
=
15
−
13
h
\newline
h
=
h =
h
=
__
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Solve for
u
u
u
.
\newline
8
u
−
8
u
+
u
=
4
8u - 8u + u = 4
8
u
−
8
u
+
u
=
4
\newline
u
=
_
_
_
u = \_\_\_
u
=
___
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Solve for
k
k
k
.
\newline
5
3
k
−
3
=
1
3
+
2
k
\frac{5}{3}k - 3 = \frac{1}{3} + 2k
3
5
k
−
3
=
3
1
+
2
k
\newline
k
=
k =
k
=
__
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Solve for
t
t
t
.
\newline
−
10
+
2
t
=
−
20
−
16
t
+
17
t
-10 + 2t = -20 - 16t + 17t
−
10
+
2
t
=
−
20
−
16
t
+
17
t
\newline
t
=
t =
t
=
____
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Solve for
k
k
k
.
\newline
−
6
k
+
5
=
−
7
-6k + 5 = -7
−
6
k
+
5
=
−
7
\newline
k
=
k =
k
=
__
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