SOLUTION: solve algebraically, using one variable. find three consecutive intergers such that three times the sum of the first two intergers is three less than seven times the third.

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Question 213735: solve algebraically, using one variable. find three consecutive intergers such that three times the sum of the first two intergers is three less than seven times the third.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Recall that consecutive integers are of the form: x, x+1, x+2, x+3, etc...


The statement: "three times the sum of the first two intergers is three less than seven times the third" translates to 3%28x%2B%28x%2B1%29%29=7%28x%2B2%29-3


3%28x%2B%28x%2B1%29%29=7%28x%2B2%29-3 Start with the given equation.


3%28x%2Bx%2B1%29=7%28x%2B2%29-3 Remove unneeded parenthesis.


3%282x%2B1%29=7%28x%2B2%29-3 Combine like terms.


6x%2B3=7x%2B14-3 Distribute.


6x%2B3=7x%2B11 Combine like terms on the right side.


6x=7x%2B11-3 Subtract 3 from both sides.


6x-7x=11-3 Subtract 7x from both sides.


-x=11-3 Combine like terms on the left side.


-x=8 Combine like terms on the right side.


x=%288%29%2F%28-1%29 Divide both sides by -1 to isolate x.


x=-8 Reduce.


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Answer:

So the solution is x=-8


This means that the three numbers are -8, -7, and -6