SOLUTION: I need help on this question! here are two consecutive integers such that the sum of one-half of the smaller integer and five times the larger integer is equal to the product of 7

Question 1004846: I need help on this question!
here are two consecutive integers such that the sum of one-half of the smaller integer and five times the larger integer is equal to the product of 7 and 1 less than the smaller integer. Find the integers.

Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
let x and x+1 be our consecutive integers, then
(x/2) + 5(x+1) = 7(x-1)
(x/2) + 5x +5 = 7x -7
add 7 to both sides of =
(x/2) +5x +12 = 7x
multiply both sides of = by 2
x +10x +24 = 14x
11x +24 = 14x
subtract 11x from both sides of =
3x = 24
x = 8
*************************************************
our two consecutive integers are 8 and 9
check the answer
(8/2) + 5(9) = 7(8-1)
49 = 49
our answer checks

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