Let n represent the number.
(8 +2n)×6 = 7n +13 . . . . . the problem statement translated to symbols
48 +12n = 7n +13 . . . . . . eliminate parentheses
35 +5n = 0 . . . . . . . . . . . subtract the right side
7 + n = 0 . . . . . . . . . . . . . divide by the coefficient of n
n = -7 . . . . . . . . . . . . . . . add the opposite of the constant
The number is -7.
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Check
8 is added to twice the number: 2·(-7) +8 = -14+8 = -6
and this sum is multiplied by 6: -6·6 = -36.
This result is the same as if the number is multiplied by 7: -7·7 = -49
and 13 is added to the product: -49+13 = -36.
Indeed, we see both results are -36, the same.
