document.write( "Question 216572: what is 3 times the smaller of two consecutive odd intergers is equal to twice the greater intergers plus thirteen \n" ); document.write( "

Algebra.Com's Answer #163520 by drj(1380) $\"\"$ $\"About$

You can put this solution on YOUR website!
What is 3 times the smaller of two consecutive odd integers is equal to twice the greater integers plus thirteen.\r
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\n" ); document.write( "\n" ); document.write( "Step 1. Let n be the smaller integer and n+2 be the larger and consecutive odd integer\r
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\n" ); document.write( "\n" ); document.write( "Step 2. Let 3n be three times the smaller of two consecutive odd integers.\r
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\n" ); document.write( "\n" ); document.write( "Step 3. Let 2(n+2) be twice the larger integers.\r
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\n" ); document.write( "\n" ); document.write( "Step 4. Then, 3n=2(n+2)+13 since 3 times the smaller of two consecutive odd integers is equal to twice the greater integers plus thirteen.\r
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\n" ); document.write( "\n" ); document.write( "Step 5. The following steps will solve the equation in Step 4.\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=17.
Graphical form: Equation $\"3n=2%2A%28n%2B2%29%2B13\"$ was fully solved.
Text form: 3n=2*(n+2)+13 simplifies to 0=0
Cartoon (animation) form: $\"simplify_cartoon%28+3n=2%2A%28n%2B2%29%2B13+%29\"$
For tutors: simplify_cartoon( 3n=2*(n+2)+13 )
If you have a website, here's a link to this solution.

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DETAILED EXPLANATION

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Look at $\"3%2An=highlight_red%28+2%2A%28n%2B2%29%2B13+%29\"$ .
Moved these terms to the left $\"highlight_green%28+-2%2A%28n%2B2%29+%29\"$ , $\"highlight_green%28+-13+%29\"$
It becomes $\"3%2An-highlight_green%28+2%2A%28n%2B2%29+%29-highlight_green%28+13+%29=0\"$ .
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Look at $\"3%2An-highlight_red%28+2%2A%28n%2B2%29+%29-13=0\"$ .
Expanded term $\"-2\"$ by using associative property on $\"%28n%2B2%29\"$
It becomes $\"3%2An-highlight_green%28+2%2An+%29-highlight_green%28+2%2A2+%29-13=0\"$ .
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Look at $\"3%2An-2%2An-highlight_red%28+2+%29%2Ahighlight_red%28+2+%29-13=0\"$ .
Multiplied numerator integers
It becomes $\"3%2An-2%2An-highlight_green%28+4+%29-13=0\"$ .
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Look at $\"3%2An-2%2An-highlight_red%28+4+%29-highlight_red%28+13+%29=0\"$ .
Added fractions or integers together
It becomes $\"3%2An-2%2An%2Bhighlight_green%28+-17+%29=0\"$ .
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Look at $\"3%2An-2%2An%2Bhighlight_red%28+-17+%29=0\"$ .
Removed extra sign in front of $\"-17\"$
It becomes $\"3%2An-2%2An-highlight_green%28+17+%29=0\"$ .
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Look at $\"highlight_red%28+3%2An+%29-highlight_red%28+2%2An+%29-17=0\"$ .
Eliminated similar terms $\"highlight_red%28+3%2An+%29\"$ , $\"highlight_red%28+-2%2An+%29\"$ replacing them with $\"highlight_green%28+%283-2%29%2An+%29\"$
It becomes $\"highlight_green%28+%283-2%29%2An+%29-17=0\"$ .
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Look at $\"highlight_red%28+%283-2%29+%29%2An-17=0\"$ .
Remove extraneous '1' from product $\"highlight_red%28+%283-2%29+%29\"$
It becomes $\"n-17=0\"$ .
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Look at $\"highlight_red%28+n-17+%29=0\"$ .
Solved linear equation $\"highlight_red%28+n-17=0+%29\"$ equivalent to n-17 =0
It becomes $\"highlight_green%28+0+%29=0\"$ .
Result: $\"0=0\"$
\n" ); document.write( "This is an equation! Solutions: n=17.

Universal Simplifier and Solver

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Done!

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\n" ); document.write( "\n" ); document.write( " $\"n=17\"$ and $\"n%2B2=19\"$ \r
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\n" ); document.write( "\n" ); document.write( "Check... $\"3n=2%28n%2B2%29%2B13\"$ = $\"3%2A17=2%2A19%2B13\"$ or $\"51=38%2B13=51\"$ ... a true statement.\r
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\n" ); document.write( "\n" ); document.write( "Step 5. ANSWER: The consecutive odd integers are 17 and 19.\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 \r
\n" ); document.write( "\n" ); document.write( "http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit \r
\n" ); document.write( "\n" ); document.write( "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 \n" ); document.write( "

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