SOLUTION: the sum of three consecutive integers is -129. find the integers.

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Question 226182: the sum of three consecutive integers is -129. find the integers.
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
The sum of three consecutive integers is -129. Find the integers.

Step 1. Let n be the first integer.

Step 2. Let n+1 and n+2 be the next two consecutive integers.

Step 3. Then, n+n+1+n+2=-129 since the sum is -129.

Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • This is an equation! Solutions: n=-44.
  • Graphical form: Equation n%2Bn%2B1%2Bn%2B2=-129 was fully solved.
  • Text form: n+n+1+n+2=-129 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+n%2Bn%2B1%2Bn%2B2=-129+%29
    For tutors: simplify_cartoon( n+n+1+n+2=-129 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at n%2Bn%2Bhighlight_red%28+1+%29%2Bn%2Bhighlight_red%28+2+%29=-129.
Added fractions or integers together
It becomes n%2Bn%2Bhighlight_green%28+3+%29%2Bn=-129.
Look at n%2Bn%2Bhighlight_red%28+3+%29%2Bn=-129.
Moved 3 to the right of expression
It becomes n%2Bn%2Bn%2Bhighlight_green%28+3+%29=-129.
Look at highlight_red%28+n+%29%2Bhighlight_red%28+n+%29%2Bhighlight_red%28+n+%29%2B3=-129.
Eliminated similar terms highlight_red%28+n+%29,highlight_red%28+n+%29,highlight_red%28+n+%29 replacing them with highlight_green%28+%281%2B1%2B1%29%2An+%29
It becomes highlight_green%28+%281%2B1%2B1%29%2An+%29%2B3=-129.
Look at %28highlight_red%28+1+%29%2Bhighlight_red%28+1+%29%2Bhighlight_red%28+1+%29%29%2An%2B3=-129.
Added fractions or integers together
It becomes %28highlight_green%28+3+%29%29%2An%2B3=-129.
Look at highlight_red%28+%28highlight_red%28+3+%29%29%2An+%29%2B3=-129.
Remove unneeded parentheses around factor highlight_red%28+3+%29
It becomes highlight_green%28+3+%29%2An%2B3=-129.
Look at 3%2An%2B3=highlight_red%28+-129+%29.
Moved these terms to the left highlight_green%28+129+%29
It becomes 3%2An%2B3%2Bhighlight_green%28+129+%29=0.
Look at 3%2An%2Bhighlight_red%28+3+%29%2Bhighlight_red%28+129+%29=0.
Added fractions or integers together
It becomes 3%2An%2Bhighlight_green%28+132+%29=0.
Look at highlight_red%28+3%2An%2B132+%29=0.
Solved linear equation highlight_red%28+3%2An%2B132=0+%29 equivalent to 3*n+132 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: n=-44.

Universal Simplifier and Solver


Done!



With n=-44, n+1=-43, and n+2=-42. Not the sum of these integers is -129.

Step 4. The integers are -44, -43, and -42.

I hope the above steps were helpful.

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And good luck in your studies!

Respectfully,
Dr J