Luttrell 2012
74
Name: ______________________
Date: _____
5a – Solving for a Variable (Multiple Variables present)
When solving for a variable, use the inverse functions. To remove a division, multiply. To
remove an addition, subtract. Here is a list of some common inverse pairs:
add
multiply
square,
cubes...
logarithms
f(x)s
trigonometr
ic f(x)s
derivatives
subtract
divide
square root,
cube root...
exponential
f(x)s
inverse trig integrals
When faced with multiple variables, just focus on the variable you need to solve for. Remove all
the terms and coefficients that surround the needed variable. Here is an example:
Solve for
b
1
:
A
b
b h
=
+
1
2
1
2
(
)
2
1
2
A
b
b h
=
+
(
)
Since
b
1
is interior, remove constants
outside
2
1
2
A
h
b
b
=
+
of the parentheses first. Undo division of 2
2
2
1
A
h
b
b
−
=
by multiplying by 2. Undo multiplication of
h
by dividing. And so forth.
1. Solve for
h
:
V = ⅓πr
2
h
2. Solve for
m
:
y = mx + b
3. Solve for
b
:
V
b h
=
1
3
2
4. Solve for
r
:
V = πr
2
h
5. Solve for
y
1
:
m
y
y
x
x
=
−
−
1
2
1
2
6. Solve for
x
1
:
m
y
y
x
x
=
−
−
1
2
1
2
7. Solve for
h
:
A = ½bh
8. Solve for
y
:
x
2
+ y
2
= r
2
