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Math Problems
Algebra 1
Rearrange multi-variable equations
Solve for
t
t
t
in terms of
u
,
v
u, v
u
,
v
, and
w
w
w
.
\newline
v
=
wut
t
=
\begin{array}{l}v=\text { wut } \\t=\end{array}
v
=
wut
t
=
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Solve for
u
u
u
in terms of
r
r
r
,
s
s
s
, and
t
t
t
.
\newline
t
=
1
2
u
(
s
+
r
)
t = \frac{1}{2}u(s + r)
t
=
2
1
u
(
s
+
r
)
\newline
u
=
u =
u
=
______
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x
+
y
=
1
x+y=1
x
+
y
=
1
,
y
+
z
=
−
1
y+z=-1
y
+
z
=
−
1
and
z
+
x
=
2
z+x=2
z
+
x
=
2
.
\newline
What is the value of
x
−
y
−
z
x-y-z
x
−
y
−
z
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Solve for
v
v
v
in terms of
w
w
w
and
x
x
x
.
\newline
w
=
x
+
v
w = x + v
w
=
x
+
v
\newline
v
=
v =
v
=
_____
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Solve for
v
v
v
in terms of
t
t
t
,
u
u
u
, and
w
w
w
.
\newline
t
=
v
+
w
+
u
t = v + w + u
t
=
v
+
w
+
u
\newline
v
=
v =
v
=
______
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Solve for
w
w
w
in terms of
v
v
v
and
x
x
x
.
\newline
x
=
−
w
v
x = -\frac{w}{v}
x
=
−
v
w
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Solve for
q
q
q
in terms of
p
p
p
and
r
r
r
.
\newline
r
=
q
−
p
r = q - p
r
=
q
−
p
\newline
q
=
q =
q
=
______
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Solve for
s
s
s
in terms of
t
t
t
,
u
u
u
, and
v
v
v
.
\newline
u
=
s
−
t
−
v
u = s - t - v
u
=
s
−
t
−
v
\newline
s
=
s =
s
=
______
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Solve for
t
t
t
in terms of
q
q
q
,
r
r
r
, and
s
s
s
.
\newline
s
=
t
−
q
+
r
s = t - q + r
s
=
t
−
q
+
r
\newline
t
=
t =
t
=
______
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Solve for
q
q
q
in terms of
p
p
p
,
r
r
r
, and
s
s
s
.
\newline
r
=
q
−
s
+
p
r = q - s + p
r
=
q
−
s
+
p
\newline
q
=
q =
q
=
______
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Solve for
x
x
x
in terms of
w
w
w
,
y
y
y
, and
z
z
z
.
\newline
y
=
z
+
w
+
x
y = z + w + x
y
=
z
+
w
+
x
\newline
x
=
x =
x
=
______
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Solve for
z
z
z
in terms of
w
w
w
,
x
x
x
, and
y
y
y
.
\newline
y
=
z
−
x
−
w
y = z - x - w
y
=
z
−
x
−
w
\newline
z
=
z =
z
=
______
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Solve for
r
r
r
in terms of
s
s
s
,
t
t
t
,
u
u
u
, and
v
v
v
.
\newline
s
u
=
−
v
r
t
su = -vrt
s
u
=
−
v
r
t
\newline
r
=
r =
r
=
_____
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Solve for
x
x
x
in terms of
v
v
v
,
w
w
w
,
y
y
y
, and
z
z
z
.
\newline
x
w
=
−
z
v
y
xw = -zvy
x
w
=
−
z
v
y
\newline
x
=
x =
x
=
______
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Solve for
u
u
u
in terms of
v
v
v
,
w
w
w
, and
x
x
x
.
\newline
w
=
−
x
v
u
w = -xvu
w
=
−
xvu
\newline
u
=
_
_
_
_
_
_
u = \_\_\_\_\_\_
u
=
______
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Solve for
q
q
q
in terms of
p
p
p
,
r
r
r
,
s
s
s
, and
t
t
t
.
\newline
q
p
=
s
r
t
qp = srt
qp
=
sr
t
\newline
q
=
q =
q
=
______
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Solve for
a
a
a
in terms of
b
b
b
and
c
c
c
.
\newline
b
=
a
c
b = ac
b
=
a
c
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Solve for
y
y
y
in terms of
v
v
v
,
w
w
w
,
x
x
x
, and
z
z
z
.
\newline
z
v
=
−
x
w
y
zv = -xwy
z
v
=
−
x
w
y
\newline
y
=
y =
y
=
______
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Solve for
r
r
r
in terms of
s
s
s
,
t
t
t
,
u
u
u
, and
v
v
v
.
\newline
v
s
=
−
t
r
u
vs = -tru
v
s
=
−
t
r
u
\newline
r
=
r =
r
=
______
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Solve for
t
t
t
in terms of
r
r
r
,
s
s
s
,
u
u
u
, and
v
v
v
.
\newline
s
v
=
u
r
t
sv = urt
s
v
=
u
r
t
\newline
t
=
t =
t
=
______
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Solve for
x
x
x
in terms of
v
v
v
and
w
w
w
.
\newline
v
=
x
+
w
v = x + w
v
=
x
+
w
\newline
x
=
x =
x
=
______
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Solve for
t
t
t
in terms of
s
s
s
,
u
u
u
,
v
v
v
, and
w
w
w
.
\newline
s
t
=
u
w
v
st = uwv
s
t
=
u
w
v
\newline
t
=
_
(
_
t = \_\\(\_
t
=
_
(
_
\\_\)
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show there exist irrational numbers
x
,
y
x, y
x
,
y
for which
x
y
x^y
x
y
is rational
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Solve for
w
w
w
in terms of
A
A
A
and .
\newline
A
=
w
A = w
A
=
w
\newline
w
=
w =
w
=
______
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Solve for
R
R
R
in terms of
P
P
P
,
V
V
V
,
n
n
n
, and
T
T
T
.
\newline
P
V
=
n
R
T
PV = nRT
P
V
=
n
RT
\newline
R
=
R =
R
=
______
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Solve for
t
t
t
in terms of
q
q
q
,
r
r
r
,
s
s
s
, and
u
u
u
.
\newline
r
u
=
t
q
s
ru = tqs
r
u
=
tq
s
\newline
t
=
t =
t
=
______
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Solve for
q
q
q
in terms of
p
p
p
,
r
r
r
,
s
s
s
, and
t
t
t
.
\newline
t
q
=
r
s
p
tq = rsp
tq
=
rs
p
\newline
q
=
q =
q
=
______
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Solve for
w
w
w
in terms of
t
t
t
,
u
u
u
,
v
v
v
, and
x
x
x
.
\newline
v
w
=
−
t
x
u
vw = -txu
v
w
=
−
t
xu
\newline
w
=
w =
w
=
______
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Solve for
t
t
t
in terms of
u
u
u
,
v
v
v
, and
w
w
w
.
\newline
v
=
−
w
u
t
v = -wut
v
=
−
w
u
t
\newline
t
=
t =
t
=
______
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Solve for
q
q
q
in terms of
r
r
r
and
s
s
s
.
\newline
r
=
−
q
s
r = -qs
r
=
−
q
s
\newline
q
=
q =
q
=
______
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Solve for
s
s
s
in terms of
p
p
p
,
q
q
q
,
r
r
r
, and
t
t
t
.
\newline
t
r
=
−
p
s
q
tr = -psq
t
r
=
−
p
s
q
\newline
s
=
s =
s
=
______
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Solve for
u
u
u
in terms of
v
v
v
,
w
w
w
, and
x
x
x
.
\newline
w
=
v
+
u
−
x
w = v + u - x
w
=
v
+
u
−
x
\newline
u
=
_
_
_
_
_
_
u = \_\_\_\_\_\_
u
=
______
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Solve for
w
w
w
in terms of
t
t
t
,
u
u
u
,
v
v
v
, and
x
x
x
.
\newline
w
x
=
t
u
v
wx = tuv
w
x
=
t
uv
\newline
w
=
w =
w
=
______
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Solve for
I
I
I
in terms of
P
P
P
and
V
V
V
.
\newline
P
=
I
V
P = IV
P
=
I
V
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Solve for
t
t
t
in terms of
r
r
r
,
s
s
s
,
u
u
u
, and
v
v
v
.
\newline
u
t
=
v
r
s
ut = vrs
u
t
=
v
rs
\newline
t
=
t =
t
=
______
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Given that
f
(
x
)
=
x
−
4
,
g
(
x
)
=
5
x
f(x)=x-4, \quad g(x)=5 x
f
(
x
)
=
x
−
4
,
g
(
x
)
=
5
x
and
h
(
x
)
=
2
f
(
x
−
3
)
+
2
g
(
x
−
2
)
h(x)=2 f(x-3)+2 g(x-2)
h
(
x
)
=
2
f
(
x
−
3
)
+
2
g
(
x
−
2
)
, then what is the value of
h
(
4
)
h(4)
h
(
4
)
?
\newline
Answer:
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Solve for
a
a
a
.
\newline
10
=
−
18
−
7
11
a
10=-18-\frac{7}{11} a
10
=
−
18
−
11
7
a
\newline
Answer:
a
=
a=
a
=
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Solve for
x
x
x
.
\newline
Assume the equation has a solution for
x
x
x
.
\newline
a
x
+
3
x
=
b
x
+
5
x
=
□
\begin{array}{l} a x+3 x=b x+5 \\ x=\square \end{array}
a
x
+
3
x
=
b
x
+
5
x
=
□
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Solve for
y
y
y
.
\newline
Assume the equation has a solution for
y
y
y
.
\newline
12
y
+
d
=
−
19
y
+
t
y
=
□
\begin{array}{l} 12 y+d=-19 y+t \\ y=\square \end{array}
12
y
+
d
=
−
19
y
+
t
y
=
□
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Solve for
y
y
y
.
\newline
Assume the equation has a solution for
y
y
y
.
\newline
p
y
+
7
=
6
y
+
q
y
=
□
\begin{array}{l} p y+7=6 y+q \\ y=\square \end{array}
p
y
+
7
=
6
y
+
q
y
=
□
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Solve for
x
x
x
.
\newline
Assume the equation has a solution for
x
x
x
.
\newline
a
⋅
(
5
−
x
)
=
b
x
−
8
x
=
□
\begin{array}{l} a \cdot(5-x)=b x-8 \\ x=\square \end{array}
a
⋅
(
5
−
x
)
=
b
x
−
8
x
=
□
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Solve for
x
x
x
.
\newline
Assume the equation has a solution for
x
x
x
.
\newline
19
x
+
r
x
=
−
37
x
+
w
x
=
□
\begin{array}{l} 19 x+r x=-37 x+w \\ x=\square \end{array}
19
x
+
r
x
=
−
37
x
+
w
x
=
□
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Solve for
z
z
z
.
\newline
Assume the equation has a solution for
z
z
z
.
\newline
16
z
+
29
z
=
p
z
−
v
16 z+29 z=p z-v
16
z
+
29
z
=
p
z
−
v
\newline
z
=
z=
z
=
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Solve for
x
x
x
.
\newline
Assume the equation has a solution for
x
x
x
.
\newline
−
p
x
+
r
=
−
8
x
−
2
x
=
□
\begin{array}{l} -p x+r=-8 x-2 \\ x=\square \end{array}
−
p
x
+
r
=
−
8
x
−
2
x
=
□
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Solve for
z
z
z
.
\newline
Assume the equation has a solution for
z
z
z
.
\newline
−
4
z
+
1
=
b
z
+
c
z
=
□
\begin{array}{l} -4 z+1=b z+c \\ z=\square \end{array}
−
4
z
+
1
=
b
z
+
c
z
=
□
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Solve for
z
z
z
.
\newline
Assume the equation has a solution for
z
z
z
.
\newline
−
c
z
+
6
z
=
t
z
+
83
z
=
□
\begin{array}{l} -c z+6 z=t z+83 \\ z=\square \end{array}
−
cz
+
6
z
=
t
z
+
83
z
=
□
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Solve for
x
x
x
.
\newline
Assume the equation has a solution for
x
x
x
.
\newline
d
⋅
(
−
3
+
x
)
=
k
x
+
9
x
=
□
\begin{array}{l} d \cdot(-3+x)=k x+9 \\ x=\square \end{array}
d
⋅
(
−
3
+
x
)
=
k
x
+
9
x
=
□
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Solve for
y
y
y
.
\newline
Assume the equation has a solution for
y
y
y
.
\newline
p
y
+
q
y
=
−
4
y
+
8
y
=
□
\begin{array}{l} p y+q y=-4 y+8 \\ y=\square \end{array}
p
y
+
q
y
=
−
4
y
+
8
y
=
□
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Solve for
z
z
z
.
\newline
Assume the equation has a solution for
z
z
z
.
\newline
−
p
⋅
(
d
+
z
)
=
−
2
z
+
59
z
=
□
\begin{array}{l} -p \cdot(d+z)=-2 z+59 \\ z=\square \end{array}
−
p
⋅
(
d
+
z
)
=
−
2
z
+
59
z
=
□
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Solve for
y
y
y
.
\newline
Assume the equation has a solution for
y
y
y
.
\newline
v
⋅
(
j
+
y
)
=
61
y
+
82
y
=
□
\begin{array}{l} v \cdot(j+y)=61 y+82 \\ y=\square \end{array}
v
⋅
(
j
+
y
)
=
61
y
+
82
y
=
□
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