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. 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 3rd added to half the 1st is 14 less than twice the 2nd} 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  Algebra House
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