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

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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?

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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

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7. f + g = h; for g 2

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8. t = -3r + s ; for s 5

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Solve for the indicated variable.

9. 3ab = c; for a

10. y = x + z ; for z 3

11. m + 3 = p; for m n

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________________________

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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