Algebraic problem......?

-3x - 7 = -47 + x

add 3x to both sides:

3x - 3x - 7 = -47 + x + 3x

0 - 7 = -47 + 4x

7 = -47 + 4x

now add 47 to both sides:

47 - 7 = 47 - 47 + 4x

40 = 0 + 4x

40 = 4x

now divide both sides by 4

40/4 = 4x/4

10 = (4/4)x

10 = (1)x

10 = x

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If you wanted to do this is really gory detail there are some additional steps. For example in the step where I went from 3x - 3x - 7 to 0 - 7 I really should have done it as follows:

3x - 3x - 7

(3 - 3)x - 7 [using the distributive property]

(0)x - 7 [definition of subtract which is the same as additive inverse]

0 - 7 [zero times anything is 0]

-7 [0 is the additive identity]

move the like terms to one side

-3x - 7 = -47 + x

-3x - x = -47 + 7

-4x = -40

x = -40 / -4

x = 10

Then you move the like terms together.

-3x - x = -47 + 7 (+x becomes -x and -7 becomes +7)

Afterwards you just solve for x.

-4x = -40

x= 10