Question 791444
<br>
Oh, my........<br>
Tutor @CubeyThePenguin: wrong equation, leading to wrong answer.<br>
Tutor @MathTherapy: nothing of use to you the student....<br>
Tutor @josgarithmetic: algebra errors, leading to wrong answer... (which she could have seen if she had bothered to check to see if her answers were right).<br>
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While there are many problems involving three consecutive integers where it is advantageous to call the numbers x-1, x, and x+1, I don't see that being helpful here.  So let the numbers be x, x+1, and x+2.  Then<br>
"...five times the third integer equals twice the first integer plus seven more than the second integer"<br>
5 times the third integer: 5(x+2)<br>
twice the first integer plus 7 more than the second integer: 2x+((x+1)+7)<br>
{{{5(x+2) = 2x+((x+1)+7)}}}
{{{5x+10 = 3x+8}}}
{{{2x = -2}}}
{{{x = -1}}}<br>
ANSWER: The three consecutive integers are -1, 0, and 1.<br>
CHECK:
5 times the third integer: 5(1) = 5<br>
twice the first integer plus 7 more than the second integer: 2(-1)+(0+7) = -2+7 = 5<br>