Name ________________________________________ Date __________________ Class__________________
LESSON
2-5
Review for Mastery
Solving for a Variable
Solving for a variable in a formula can make it easier to use that formula. The process is
similar to that of solving multi-step equations. Find the operations being performed on the
variable you are solving for, and then use inverse operations.
Operations
Solve using Inverse Operations
A = lw
Solve for w.
• w is multiplied by l.
• Divide both sides by l.
P = 2l + 2w
Solve for w.
• w is multiplied by 2.
• Add −2l to both sides.
• Then 2l is added.
• Then divide both sides by 2.
1
bh relates the area A of a triangle
2
to its base b and height h. Solve the formula for b.
The formula A =
A=
⎛ 2⎞
⎜ ⎟ •A=
⎝ 1⎠
1
bh
2
b is multiplied by
⎛ 2⎞ 1
⎜ ⎟ bh
⎝ 1⎠ 2
Multiply both sides by
2A = bh
1
.
2
The order of the inverse
operations is the order of
operations in reverse.
2
.
1
b is multiplied by h.
bh
2A
=
h
h
Divide both sides by h.
2A
=b
h
Simplify.
Solve for the indicated variable.
1. P = 4s for s
________________________
2. a + b + c = 180 for b
_________________________
3. P =
KT
for K
V
________________________
1
lwh relates the volume of a square pyramid
3
to its base length l, base width w, and height h.
The formula V =
4. Solve the formula for w.
___________________________
5. A square pyramid has a volume of 560 in3, a base length
of 10 in., and a height of 14 in. What is its base width?
___________________________
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
2-38
Holt McDougal Algebra 1
Name ________________________________________ Date __________________ Class__________________
Review for Mastery
LESSON
2-5
Solving for a Variable continued
Any equation with two or more variables can be solved for any given variable.
Solve x =
x=
y −z
for y.
10
y−z
10
⎛y − z⎞
10(x) = 10 ⎜
⎟
⎝ 10 ⎠
10x = y − z
+z
y − z is divided by 10.
Multiply both sides by 10.
z is subtracted from y. Add z to both sides.
+z
10x + z = y
Solve a = b +
a=b+
−b
a−b=
c
for c.
d
c
d
−b
Add −b to each side.
c
d
⎛c ⎞
d(a − b) = ⎜ ⎟ d
⎝d ⎠
Multiply both sides by d.
d(a − b) = c
Simplify.
State the first inverse operation to perform when solving for the
indicated variable.
6. y = x + z; for z
7.
_________________________________________________________
f +g
= h; for g
2
8. t = −3r +
_________________________________________________________
s
; for s
5
_________________________________________________________
Solve for the indicated variable.
9. 3ab = c; for a
________________________
10. y = x +
z
; for z
3
_________________________
11.
m+3
= p; for m
n
________________________
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
2-39
Holt McDougal Algebra 1
Practice C
1. w =
P − 2l
2
g
3. f =
−3
Reading Strategies
6. h =
jk + g
5
7. r = s(t − 9)
8. n =
m+3
p
F
9. a. a =
m
2. The equation contains only one
variable, n.
4. a = 12 − 5b
z + 7y
3
5. x =
1. Possible answer: 3x + 2y = 9
2. vf = at + vi
3. Yes, because it has two or more
variables.
4. Divide both sides by r.
b−8
5. t =
3
V
Iw
b. 3 cm
I
10. a. t =
Pr
b. 19 m/s2
6. a. h =
b. 8 years
LESSON 2-6
Review for Mastery
1. s =
P
4
VP
3. K =
T
Practice A
2. b = 180 − a – c
1. −3; 2; −2; 2
3V
4. w =
lh
2. −7; 7; 4; 4; 4; 4; −11; 3
3. 6; −6; 6; −5; 7
5. 12 in.
6. add –x to both sides
7. multiply both sides by 2
8. add 3r to both sides
c
9. a =
3b
10. z = 3(y − x)
8. {−11, 7}
9. {−1, 11}
11. {−7, 3}
14. 22 miles per gallon; 26 miles per gallon
2. P = 2000
Practice B
1. {−12, 12}
4. r = 0.032 or 3.2%
5. $351
6. 3 years
7. $2200
8. 0.03 or 3%
2.
1 1
− ,
2 2
3. {−10, 10}
10. 5 years
4. {−9, 9}
11. 0.027 or 2.7%
5. {−8, 8}
6. {−13, 7}
Problem Solving
d
t
7. {−17, 17}
13. x − 24 = 2
3. t = 5 years
1. r =
6. {−9, 9}
12. {−11, 9}
Challenge
9. $247
5. {−14, 14}
10. {−5, 5}
11. m = pn − 3
1. l = 375
4. {−8, 8}
7. {−1, 3}
2. 9.1 m/s
3. 8.5 m/s
4. 0.4 m/s
5. B
6. F
7. D
8. J
8. {2, 8}
9. {−14, 10}
10. {−3, 3}
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
A18
Holt McDougal Algebra 1