2-5 Solving for a Variable - Rochester City School District
Name ________________________________________ Date __________________ Class__________________
LESSON Review for Mastery
2-5 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.
A = lw Solve for w.
P = 2l + 2w Solve for w.
Operations ? w is multiplied by l.
? w is multiplied by 2. ? Then 2l is added.
Solve using Inverse Operations ? Divide both sides by l.
? Add -2l to both sides. ? Then divide both sides by 2.
The
formula
A
=
1 2
bh
relates
the
area
A
of a triangle
to its base b and height h. Solve the formula for b.
A = 1 bh 2
21
?
A
=
2 1
1 2
bh
b is multiplied by 1 . 2
Multiply both sides by 2 . 1
2A = bh
b is multiplied by h.
2A = bh 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
The order of the inverse operations is the order of operations in reverse.
3. P = KT for K V
________________________
_________________________
________________________
The
formula
V
=
1 3
lwh
relates
the
volume
of a
square pyramid
to its base length l, base width w, and height h.
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__________________
LESSON Review for Mastery
2-5 Solving for a Variable continued
Any equation with two or more variables can be solved for any given variable.
Solve x =
y -z 10
for y.
x= y-z 10
10(x)
=
10
y
-
z
10
y - z is divided by 10. Multiply both sides by 10.
10x = y - z
z is subtracted from y. Add z to both sides.
+z +z
10x + z = y
Solve a = b +
c d
for c.
a=b+ c d
-b -b
a-b= c d
d(a
-
b)
=
c
d
d
d(a - b) = c
Add -b to each side.
Multiply both sides by d. 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
3.
f
=
g - 3
5.
x =
z + 7y 3
7. r = s(t - 9)
2. vf = at + vi
4. a = 12 - 5b
6.
h =
jk + g 5
8.
n
=
m+3 p
9.
a. a
=
F m
b. 19 m/s2
10.
a.
t
=
I Pr
b. 8 years
Review for Mastery
1.
s =
P 4
2. b = 180 - a ? c
3.
K
=
VP T
4.
w =
3V lh
5. 12 in.
6. add ?x to both sides
7. multiply both sides by 2
8. add 3r to both sides
9.
a
=
c 3b
10. z = 3(y - x)
11. m = pn - 3
Challenge 1. l = 375 3. t = 5 years 4. r = 0.032 or 3.2% 5. $351 7. $2200 9. $247
11. 0.027 or 2.7%
2. P = 2000
6. 3 years 8. 0.03 or 3% 10. 5 years
Problem Solving
1.
r
=
d t
3. 8.5 m/s
5. B
7. D
2. 9.1 m/s
4. 0.4 m/s 6. F 8. J
Reading Strategies
1. Possible answer: 3x + 2y = 9
2. The equation contains only one variable, n.
3. Yes, because it has two or more variables.
4. Divide both sides by r.
5.
t =
b-8 3
6.
a.
h
=
V Iw
b. 3 cm
LESSON 2-6
Practice A
1. -3; 2; -2; 2
2. -7; 7; 4; 4; 4; 4; -11; 3
3. 6; -6; 6; -5; 7
4. {-8, 8}
5. {-14, 14}
6. {-9, 9}
7. {-17, 17}
8. {-11, 7}
9. {-1, 11}
10. {-5, 5}
11. {-7, 3}
12. {-11, 9}
13. x - 24 = 2
14. 22 miles per gallon; 26 miles per gallon
Practice B 1. {-12, 12}
2. - 1 , 1 22
3. {-10, 10} 4. {-9, 9} 5. {-8, 8} 6. {-13, 7} 7. {-1, 3} 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
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