Question 774554
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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