document.write( "Question 224489: find three consecutive even integers such that twice largest integer exceeds the sum of the sum of the first two by 6. \n" ); document.write( "

Algebra.Com's Answer #167742 by drj(1380) $\"\"$ $\"About$

You can put this solution on YOUR website!
Find three consecutive even integers such that twice largest integer exceeds the sum of the sum of the first two by 6.\r
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\n" ); document.write( "\n" ); document.write( "Step 1. Let n be the first even integer.\r
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\n" ); document.write( "\n" ); document.write( "Step 2. Let n+2 and n+4 be the next two even integers.\r
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\n" ); document.write( "\n" ); document.write( "Step 3. Let 2(n+4)=2n+8 be twice the largest integer.\r
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\n" ); document.write( "\n" ); document.write( "Step 4. Let n+n+2=2n+2 be the sum of the first two.\r
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\n" ); document.write( "\n" ); document.write( "Step 5. Then, 2n+8=2n+2+6 since twice largest integer exceeds the sum of the sum of the first two by 6.\r
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\n" ); document.write( "\n" ); document.write( "Step 6. Solving the equation in Step 5 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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Graphical form: Equation $\"2n%2B8=2n%2B2%2B6\"$ was fully solved.
Text form: 2n+8=2n+2+6 simplifies to 0=0
Cartoon (animation) form: $\"simplify_cartoon%28+2n%2B8=2n%2B2%2B6+%29\"$
For tutors: simplify_cartoon( 2n+8=2n+2+6 )
If you have a website, here's a link to this solution.

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DETAILED EXPLANATION

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Look at $\"2%2An%2B8=2%2An%2Bhighlight_red%28+2+%29%2Bhighlight_red%28+6+%29\"$ .
Added fractions or integers together
It becomes $\"2%2An%2B8=2%2An%2Bhighlight_green%28+8+%29\"$ .
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Look at $\"2%2An%2B8=highlight_red%28+2%2An%2B8+%29\"$ .
Moved these terms to the left $\"highlight_green%28+-2%2An+%29\"$ , $\"highlight_green%28+-8+%29\"$
It becomes $\"2%2An%2B8-highlight_green%28+2%2An+%29-highlight_green%28+8+%29=0\"$ .
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Look at $\"2%2An%2Bhighlight_red%28+8+%29-2%2An-highlight_red%28+8+%29=0\"$ .
Added fractions or integers together
It becomes $\"2%2An%2Bhighlight_green%28+0+%29-2%2An=0\"$ .
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Look at $\"2%2An%2Bhighlight_red%28+0+%29-2%2An=0\"$ .
Moved $\"0\"$ to the right of expression
It becomes $\"2%2An-2%2An%2Bhighlight_green%28+0+%29=0\"$ .
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Look at $\"2%2An-2%2An%2Bhighlight_red%28+0+%29=0\"$ .
Remove extraneous zero $\"highlight_red%28+0+%29\"$
It becomes $\"2%2An-2%2An=0\"$ .
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Look at $\"highlight_red%28+2%2An+%29-highlight_red%28+2%2An+%29=0\"$ .
Eliminated similar terms $\"highlight_red%28+2%2An+%29\"$ , $\"highlight_red%28+-2%2An+%29\"$ replacing them with $\"highlight_green%28+%282-2%29%2An+%29\"$
It becomes $\"highlight_green%28+%282-2%29%2An+%29=0\"$ .
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Look at $\"highlight_red%28+%282-2%29%2An+%29=0\"$ .
Since $\"highlight_red%28+%282-2%29%2An+%29\"$ has zero as a factor, it should be replaced with a zero
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Look at $\"0=0\"$ .
Added fractions or integers together
It becomes $\"0=0\"$ .
Result: $\"0=0\"$
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Universal Simplifier and Solver

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Done!

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\n" ); document.write( "\n" ); document.write( "Step 7. ANSWER: The three consecutive integers can be anything that the satisfies equation in Step 5. \r
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\n" ); document.write( "\n" ); document.write( "For example 2, 4, 6 will yield 2(6)=2+4+6 which is a true statement\r
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\n" ); document.write( "\n" ); document.write( "Another example, 20, 22, 24 will yield 2(24)=20+22+6 which is another true statement\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 \n" ); document.write( "

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