To solve a formula for a specified variable, we use the samesteps that we used
to solve an equation with just one variable. For example, solve the following for x.
124 CHAPTER 2 Linear Equations and Inequalities in One Variable
NOW TRY
EXERCISE 6
Solve for W=Fd F.
Subtract 4.Divide by 3.x= 3
3 x
3
=
9
3
3 x= 9
3 x+ 4 - 4 = 13 - 4
3 x+ 4 = 13
Subtract b.Divide by a.x=
c-b
a
ax
a
=
c-b
a
ax= c- b
ax+ b- b= c- b
ax+ b= c
When solving a formula for a specified variable, we treat the specified variable as if
it were the ONLY variable, and treat the other variables as if they were numbers.
Equation
solved for x Formula
solved for xSolving for a Specified VariableSolve for W.
Wis multiplied by L, so undo the multiplication by dividing each side by L.
Divide by L.or W= LWL =LL#W= 1 #W=W
a
L
a
L
=W,
a
L
=
LW
L
a=LW
a= LW
EXAMPLE 6
NOW TRY
EXERCISE 7
Solve for Ax+By=C A.
NOW TRY
EXERCISE 8
Solve for x=u+zs z.
Our goal is
to isolate W.NOW TRYSolving for a Specified VariableSolve for L.
Subtract 2W.
Combine like terms.Divide by 2.or L=^22 L=^22 #L= 1 #L=L
P- 2 W
2
P- 2 W
2
=L,
P- 2 W
2
=
2 L
2
P- 2 W= 2 L
P- 2 W= 2 L+ 2 W- 2 W
P= 2 L+ 2 W
P= 2 L+ 2 W
EXAMPLE 7
NOW TRYSolving for a Specified VariableSolve for C.
Subtract 32.Multiply byor C=
5
9
1 F- 322
5
9
1 F- 322 =C,
59.
5
9
1 F- 322 =
5
9
#^9
5
C
F- 32 =
9
5
C
F- 32 =
9
5
C+ 32 - 32
F=
9
5
C+ 32
F=^95 C+ 32
EXAMPLE 8
Our goal is
to isolate L.This is the formula for converting
temperatures from Celsius to
Fahrenheit.This is the formula for converting
temperatures from Fahrenheit to
Celsius.Our goal is
to isolate C.Be sure to use
parentheses.NOW TRYNOW TRY ANSWERS
- z=x-su
A=
C-By
F= x
W
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