Name ________________________________________ Date __________________ Class __________________
LESSON
4-3
Solving for a Variable
Reteach
Solving for a variable in a formula can make it easier to use.
You can solve a formula, or literal equation, for any one of the variables.
To solve a literal equation or formula, underline the variable you are solving for, and then
UNDO what has been done to that variable. Use inverse operations in the same way you do
when solving an equation or inequality.
The formula for finding the area of a rectangle when you know length and width is A = lw.
If you know the area and the length, you could find the width by using a formula for w.
Examples
Solve A = lw for w.
A Iw
=
I
I
A
A
= w or w =
I
I
y −b
Solve
= x for b.
m
y −b
= x (m)
(m )
m
y − b = xm
−y
−y
Since w is multiplied by l, use division to undo this.
Divide both sides by l.
What has been done to b? First undo dividing by m.
Multiply both sides by m.
Subtract y from both sides.
− b = xm − y
Finally, multiply both sides by −1 to solve for b.
(−1) (−b) = (−1) (xm − y)
b = − xm + y or b = y − xm
Solve each formula for the indicated variable.
1. A =
1
(a + b )h, for b
2
________________________
4. P = 2l + 2w, for w
________________________
2. d = rt, for r
3. P =
_______________________
5. V =
1
lwh, for h
3
3 x + 10n + 9
, for x
3
________________________
6. P =
_______________________
KT
, for K
V
________________________
Solve each equation for the indicated variable.
7. a + b + c = 180, for b
________________________
10. x =
y −z
, for y
10
________________________
8. x = ay + a , for y
_______________________
11. a = b +
c
, for c
d
_______________________
9.
m p
= , for m
n q
________________________
12. y = x +
z
, for x
3
________________________
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
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