Simplify and solve each of the following equations.

a. d + d + 10 = 50

b. 30 - f + 8f = 30

c. - 12 = 4e + 23 + e

d. 42 = 32 - 6f - 4f

Step-by-step explanation:

a) d + d + 10 = 50

2d + 10 = 50

2d = 50 - 10

2d = 40

d = 40/2

d = 20

b) 30 - f + 8f = 30

30 + 7f = 30

7f = 30 - 30

7f = 0

f = 0

c) - 12 = 4e + 23 + e

-12 = 5e + 23

5e + 23 = - 12

5e = - 12 - 23

5e = - 35

e = - 35/5

e = - 7

d) 42 = 32 - 6f - 4f

42 = 32 - 10f

32 - 10f = 42

-10f = 42 - 32

-10f = 10

f = 10/-10

f = - 1

a. d=20

b. f=0

c. e=-7

d. f=-1

Step-by-step explanation:

A. d+d+10=50

2d+10=50

Substrate 10 from both sides

2d=40

Divide both sides by 2

d=20

B. 30-f+8f=30

30+7f=30

Substrate both sides by 30

7f=0

Divide both sides by 7

f=0

C.-12=4e+23+e

Collect like terms

-12-23=4e+e

-35=5e

Divide both sides by 5

e=-7

D. 42=32-6f-4f

Collect like terms

42-32=-6f-4f

10=-10f

Divide both sides by 10

F=-1