Twice the sum of a number and 7 is equal to three times the difference of the number and 8.

First, set up what you know. Twice the sum of a number and seven means: 2x+7. Three times the difference of the number and 8 is 3(x-8).

Set both of them equal to each other and you'll get this:
2x+7 = 3(x-8)
Afterwards just follow through with algebra.
2x+7 = 3x - 24

2x + 31 = 3x

31 = 3x - 2x

31 = x

Afterwards check your work to see if it is correct.
2(31) + 7 = 3( 31 - 8 )

62 + 7 = 3(23)

69 = 69

What do you mean by that?

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