document.write( "Question 221413: there are 5 consecutive odd integers.
\n" ); document.write( "the sum of the 1st and 5th are 1 less than 3 times the fourth.
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Algebra.Com's Answer #166071 by drj(1380) $\"\"$ $\"About$

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?\r
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\n" ); document.write( "\n" ); document.write( "Step 1. Let n be a the first odd integer.\r
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\n" ); document.write( "\n" ); document.write( "Step 2. Let n+2, n+4, n+6, and n+8 be the next 4 consecutive odd integer.\r
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\n" ); document.write( "\n" ); document.write( "Step 3. Let n+n+8 be the sum of the 1st and 5th integer.\r
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\n" ); document.write( "\n" ); document.write( "Step 4. Let 3(n+6)-1 be 1 less than 3 times the fourth.\r
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\n" ); document.write( "\n" ); document.write( "Step 5. Then $\"n%2Bn%2B8=3%28n%2B6%29-1\"$ . Solving yields the following steps.\r
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Solved by pluggable solver: EXPLAIN simplification of an expression

Your Result:

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\n" ); document.write( " YOUR ANSWER\n" ); document.write( "

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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.

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DETAILED EXPLANATION

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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 $\"highlight_green%28+%281%2B1%29%2An+%29%2B8=3%2A%28n%2B6%29-1\"$ .
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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 $\"%28highlight_green%28+2+%29%29%2An%2B8=3%2A%28n%2B6%29-1\"$ .
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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 $\"highlight_green%28+2+%29%2An%2B8=3%2A%28n%2B6%29-1\"$ .
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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 $\"2%2An%2B8-highlight_green%28+3%2A%28n%2B6%29+%29%2Bhighlight_green%28+1+%29=0\"$ .
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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 $\"2%2An%2Bhighlight_green%28+9+%29-3%2A%28n%2B6%29=0\"$ .
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Look at $\"2%2An%2Bhighlight_red%28+9+%29-3%2A%28n%2B6%29=0\"$ .
Moved $\"9\"$ to the right of expression
It becomes $\"2%2An-3%2A%28n%2B6%29%2Bhighlight_green%28+9+%29=0\"$ .
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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 $\"2%2An-highlight_green%28+3%2An+%29-highlight_green%28+3%2A6+%29%2B9=0\"$ .
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Look at $\"2%2An-3%2An-highlight_red%28+3+%29%2Ahighlight_red%28+6+%29%2B9=0\"$ .
Multiplied numerator integers
It becomes $\"2%2An-3%2An-highlight_green%28+18+%29%2B9=0\"$ .
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Look at $\"2%2An-3%2An-highlight_red%28+18+%29%2Bhighlight_red%28+9+%29=0\"$ .
Added fractions or integers together
It becomes $\"2%2An-3%2An%2Bhighlight_green%28+-9+%29=0\"$ .
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Look at $\"2%2An-3%2An%2Bhighlight_red%28+-9+%29=0\"$ .
Removed extra sign in front of $\"-9\"$
It becomes $\"2%2An-3%2An-highlight_green%28+9+%29=0\"$ .
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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 $\"highlight_green%28+%282-3%29%2An+%29-9=0\"$ .
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Look at $\"%28highlight_red%28+2+%29-highlight_red%28+3+%29%29%2An-9=0\"$ .
Added fractions or integers together
It becomes $\"%28highlight_green%28+-1+%29%29%2An-9=0\"$ .
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Look at $\"%28highlight_red%28+-1+%29%29%2An-9=0\"$ .
Removed extra sign in front of $\"-1\"$
It becomes $\"%28-highlight_green%28+1+%29%29%2An-9=0\"$ .
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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 $\"-highlight_green%28+1+%29%2An-9=0\"$ .
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Look at $\"-highlight_red%28+1+%29%2An-9=0\"$ .
Remove extraneous '1' from product $\"highlight_red%28+1+%29\"$
It becomes $\"-n-9=0\"$ .
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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: $\"0=0\"$
\n" ); document.write( "This is an equation! Solutions: n=-9.

Universal Simplifier and Solver

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Done!

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\n" ); document.write( "\n" ); document.write( "n=-9, n+2=-7, n+4=-5, n+6=-3, and n+8=-1.\r
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\n" ); document.write( "\n" ); document.write( "Check Equation $\"n%2Bn%2B8=3%28n%2B6%29-1\"$ or -9+(-1)=3*(-3)-1 which is a true statement.\r
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\n" ); document.write( "\n" ); document.write( "Step 6. ANSWER: The five consecutive odd integers are -9, -7, -5, -3, and -1.\r
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\n" ); document.write( "\n" ); document.write( "I hope the above steps were helpful.\r
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\n" ); document.write( "\n" ); document.write( "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.\r
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\n" ); document.write( "\n" ); document.write( "Good luck in your studies!\r
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\n" ); document.write( "\n" ); document.write( "Respectfully,
\n" ); document.write( "Dr J
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