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

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step-by-step explanation: