SOLUTION: Find three consecutive integers such three times the third integer added to one half of the first integer is 14 less than twice the second integer.

Question 774554: Find three consecutive integers such three times the third integer added to one half of the first integer is 14 less than twice the second integer.
Answer by algebrahouse.com(1659) (Show Source): You can put this solution on YOUR website!
x = first
x + 1 = second {consecutive integers increase by 1 each time}
x + 2 = third

3(x + 2) + 0.5x = 2(x + 1) - 14 {three times the third added to half the first is 14 less than twice the second}
3x + 6 + 0.5x = 2x + 2 - 14 {used distributive property}
3.5x + 6 = 2x - 12 {combined like terms}
1.5x = -18 {subtracted 2x and 6 from each side}
x = -12 {divided each side by 1.5}
x + 1 = -11 {substituted -12, in for x, into x + 1}
x + 2 = -10 {substituted -12, in for x, into x + 2}

-12, -11, and -10 are the three consecutive integers

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