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© 2014 Pacific Crest
97
M
odel
2: S
olving
a
L
iteral
E
quation
for
a
G
iven
V
ariable
Scenario:
Solve the literal equation for
r:
7 2
3
rw r
π
− =
Step
Model
1.
Choose the variable to solve for
The variables are
r
and
w
. The symbol π is a
constant. We are to solve for
r
.
2.
Clear parentheses
There are no parentheses.
3.
Clear fractions
7 2
3
LCD is 3
7 6 3
rw r
rw r
π
π
− =
− =
4.
Combine like terms and simplify
There is nothing to simplify.
5.
Isolate the variable
(
) (
)
(
)
(
)
(
)
(
)
7 6
3
7 3 6
7 3 6
7
3 6
7
7
or
3 2
3 2
rw r
r rw
w r
r
w
r
r
w
w
−
=
= +
= +
=
+
=
=
+
+
π
π
π
π
π
π
6.
Validate
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
7 2
3
7
7
7
2
3 3 2
3 2
7 14
7
3 3 2 3 2
7 2 14
7
3 2
3 2
7 14 14
7
3 2
3 2
7
7
3 2 3 2
rw r
w
w
w
w
w
w
w w
w
w
w w
w
w
w
w
− =
−
=
+
+
−
=
+
+
+ −
=
+
+
+ −
=
+
+
=
+
+
π
π
π
π
π
π
π
π
π
π
π
π
π
π
π
π
π
π
π
2.4 Solving an Equation