SOLUTION: there are 5 consecutive odd integers. the sum of the 1st and 5th are 1 less than 3 times the fourth. what are the 5 consecutive odd integers?

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Question 221413: there are 5 consecutive odd integers.
the sum of the 1st and 5th are 1 less than 3 times the fourth.
what are the 5 consecutive odd integers?
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
There are 5 consecutive odd integers. The sum of the 1st and 5th is 1 less than 3 times the fourth. What are the 5 consecutive odd integers?

Step 1. Let n be a the first odd integer.

Step 2. Let n+2, n+4, n+6, and n+8 be the next 4 consecutive odd integer.

Step 3. Let n+n+8 be the sum of the 1st and 5th integer.

Step 4. Let 3(n+6)-1 be 1 less than 3 times the fourth.

Step 5. Then n%2Bn%2B8=3%28n%2B6%29-1. Solving yields the following steps.

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


YOUR ANSWER


  • This is an equation! Solutions: n=-9.
  • Graphical form: Equation n%2Bn%2B8=3%2A%28n%2B6%29-1 was fully solved.
  • Text form: n+n+8=3*(n+6)-1 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+n%2Bn%2B8=3%2A%28n%2B6%29-1+%29
    For tutors: simplify_cartoon( n+n+8=3*(n+6)-1 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+n+%29%2Bhighlight_red%28+n+%29%2B8=3%2A%28n%2B6%29-1.
Eliminated similar terms highlight_red%28+n+%29,highlight_red%28+n+%29 replacing them with highlight_green%28+%281%2B1%29%2An+%29
It becomes highlight_green%28+%281%2B1%29%2An+%29%2B8=3%2A%28n%2B6%29-1.
Look at %28highlight_red%28+1+%29%2Bhighlight_red%28+1+%29%29%2An%2B8=3%2A%28n%2B6%29-1.
Added fractions or integers together
It becomes %28highlight_green%28+2+%29%29%2An%2B8=3%2A%28n%2B6%29-1.
Look at highlight_red%28+%28highlight_red%28+2+%29%29%2An+%29%2B8=3%2A%28n%2B6%29-1.
Remove unneeded parentheses around factor highlight_red%28+2+%29
It becomes highlight_green%28+2+%29%2An%2B8=3%2A%28n%2B6%29-1.
Look at 2%2An%2B8=highlight_red%28+3%2A%28n%2B6%29-1+%29.
Moved these terms to the left highlight_green%28+-3%2A%28n%2B6%29+%29,highlight_green%28+1+%29
It becomes 2%2An%2B8-highlight_green%28+3%2A%28n%2B6%29+%29%2Bhighlight_green%28+1+%29=0.
Look at 2%2An%2Bhighlight_red%28+8+%29-3%2A%28n%2B6%29%2Bhighlight_red%28+1+%29=0.
Added fractions or integers together
It becomes 2%2An%2Bhighlight_green%28+9+%29-3%2A%28n%2B6%29=0.
Look at 2%2An%2Bhighlight_red%28+9+%29-3%2A%28n%2B6%29=0.
Moved 9 to the right of expression
It becomes 2%2An-3%2A%28n%2B6%29%2Bhighlight_green%28+9+%29=0.
Look at 2%2An-highlight_red%28+3%2A%28n%2B6%29+%29%2B9=0.
Expanded term -3 by using associative property on %28n%2B6%29
It becomes 2%2An-highlight_green%28+3%2An+%29-highlight_green%28+3%2A6+%29%2B9=0.
Look at 2%2An-3%2An-highlight_red%28+3+%29%2Ahighlight_red%28+6+%29%2B9=0.
Multiplied numerator integers
It becomes 2%2An-3%2An-highlight_green%28+18+%29%2B9=0.
Look at 2%2An-3%2An-highlight_red%28+18+%29%2Bhighlight_red%28+9+%29=0.
Added fractions or integers together
It becomes 2%2An-3%2An%2Bhighlight_green%28+-9+%29=0.
Look at 2%2An-3%2An%2Bhighlight_red%28+-9+%29=0.
Removed extra sign in front of -9
It becomes 2%2An-3%2An-highlight_green%28+9+%29=0.
Look at highlight_red%28+2%2An+%29-highlight_red%28+3%2An+%29-9=0.
Eliminated similar terms highlight_red%28+2%2An+%29,highlight_red%28+-3%2An+%29 replacing them with highlight_green%28+%282-3%29%2An+%29
It becomes highlight_green%28+%282-3%29%2An+%29-9=0.
Look at %28highlight_red%28+2+%29-highlight_red%28+3+%29%29%2An-9=0.
Added fractions or integers together
It becomes %28highlight_green%28+-1+%29%29%2An-9=0.
Look at %28highlight_red%28+-1+%29%29%2An-9=0.
Removed extra sign in front of -1
It becomes %28-highlight_green%28+1+%29%29%2An-9=0.
Look at highlight_red%28+%28-highlight_red%28+1+%29%29%2An+%29-9=0.
Remove unneeded parentheses around factor highlight_red%28+1+%29
It becomes -highlight_green%28+1+%29%2An-9=0.
Look at -highlight_red%28+1+%29%2An-9=0.
Remove extraneous '1' from product highlight_red%28+1+%29
It becomes -n-9=0.
Look at highlight_red%28+-n-9+%29=0.
Solved linear equation highlight_red%28+-n-9=0+%29 equivalent to -n-9 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: n=-9.

Universal Simplifier and Solver


Done!



n=-9, n+2=-7, n+4=-5, n+6=-3, and n+8=-1.

Check Equation n%2Bn%2B8=3%28n%2B6%29-1 or -9+(-1)=3*(-3)-1 which is a true statement.

Step 6. ANSWER: The five consecutive odd integers are -9, -7, -5, -3, and -1.

I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J