document.write( "Question 213912: find the three consecutive odd integers such that the sum of the first two odd integers exceeds the third by 9. \n" ); document.write( "

Algebra.Com's Answer #161572 by drj(1380) $\"\"$ $\"About$

You can put this solution on YOUR website!
Find the three consecutive odd integers such that the sum of the first two odd integers exceeds the third by 9.\r
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\n" ); document.write( "\n" ); document.write( "Step 1. Let n be an odd integer, n+2 and n+4 be the next two consecutive odd integers.\r
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\n" ); document.write( "\n" ); document.write( "Step 2. Let n+n+2 is the sum of the first two integers\r
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\n" ); document.write( "\n" ); document.write( "Step 3. Then, n+n+2=n+4+9 Since the sum of n+n+2 is 9 more than the third integer given as n+4\r
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\n" ); document.write( "\n" ); document.write( "Step 4. Solve the above equation using 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=11.
Graphical form: Equation $\"n%2Bn%2B2=n%2B4%2B9\"$ was fully solved.
Text form: n+n+2=n+4+9 simplifies to 0=0
Cartoon (animation) form: $\"simplify_cartoon%28+n%2Bn%2B2=n%2B4%2B9+%29\"$
For tutors: simplify_cartoon( n+n+2=n+4+9 )
If you have a website, here's a link to this solution.

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DETAILED EXPLANATION

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Look at $\"highlight_red%28+n+%29%2Bhighlight_red%28+n+%29%2B2=n%2B4%2B9\"$ .
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 $\"highlight_green%28+%281%2B1%29%2An+%29%2B2=n%2B4%2B9\"$ .
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Look at $\"%28highlight_red%28+1+%29%2Bhighlight_red%28+1+%29%29%2An%2B2=n%2B4%2B9\"$ .
Added fractions or integers together
It becomes $\"%28highlight_green%28+2+%29%29%2An%2B2=n%2B4%2B9\"$ .
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Look at $\"highlight_red%28+%28highlight_red%28+2+%29%29%2An+%29%2B2=n%2B4%2B9\"$ .
Remove unneeded parentheses around factor $\"highlight_red%28+2+%29\"$
It becomes $\"highlight_green%28+2+%29%2An%2B2=n%2B4%2B9\"$ .
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Look at $\"2%2An%2B2=n%2Bhighlight_red%28+4+%29%2Bhighlight_red%28+9+%29\"$ .
Added fractions or integers together
It becomes $\"2%2An%2B2=n%2Bhighlight_green%28+13+%29\"$ .
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Look at $\"2%2An%2B2=highlight_red%28+n%2B13+%29\"$ .
Moved these terms to the left $\"highlight_green%28+-n+%29\"$ , $\"highlight_green%28+-13+%29\"$
It becomes $\"2%2An%2B2-highlight_green%28+n+%29-highlight_green%28+13+%29=0\"$ .
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Look at $\"2%2An%2Bhighlight_red%28+2+%29-n-highlight_red%28+13+%29=0\"$ .
Added fractions or integers together
It becomes $\"2%2An%2Bhighlight_green%28+-11+%29-n=0\"$ .
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Look at $\"2%2An%2Bhighlight_red%28+-11+%29-n=0\"$ .
Moved $\"-11\"$ to the right of expression
It becomes $\"2%2An-n%2Bhighlight_green%28+-11+%29=0\"$ .
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Look at $\"2%2An-n%2Bhighlight_red%28+-11+%29=0\"$ .
Removed extra sign in front of $\"-11\"$
It becomes $\"2%2An-n-highlight_green%28+11+%29=0\"$ .
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Look at $\"highlight_red%28+2%2An+%29-highlight_red%28+n+%29-11=0\"$ .
Eliminated similar terms $\"highlight_red%28+2%2An+%29\"$ , $\"highlight_red%28+-n+%29\"$ replacing them with $\"highlight_green%28+%282-1%29%2An+%29\"$
It becomes $\"highlight_green%28+%282-1%29%2An+%29-11=0\"$ .
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Look at $\"highlight_red%28+%282-1%29+%29%2An-11=0\"$ .
Remove extraneous '1' from product $\"highlight_red%28+%282-1%29+%29\"$
It becomes $\"n-11=0\"$ .
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Look at $\"highlight_red%28+n-11+%29=0\"$ .
Solved linear equation $\"highlight_red%28+n-11=0+%29\"$ equivalent to n-11 =0
It becomes $\"highlight_green%28+0+%29=0\"$ .
Result: $\"0=0\"$
\n" ); document.write( "This is an equation! Solutions: n=11.

Universal Simplifier and Solver

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Done!

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\n" ); document.write( "\n" ); document.write( "Step 5. ANSWER: So the integers are 11, 13 and 15.\r
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\n" ); document.write( "\n" ); document.write( "Check 11+13=24 which is 9 more than 15. So it checks!\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 on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.\r
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\n" ); document.write( "\n" ); document.write( "And 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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