document.write( "Question 216532: $\"+5%2F2%2Ar%2B5%2F2%2A%28r%2B6%29=135+\"$ \n" ); document.write( "

Algebra.Com's Answer #163499 by ichudov(507) $\"\"$ $\"About$

You can put this solution on YOUR website!
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Solved by pluggable solver: EXPLAIN simplification of an expression

Your Result:

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This is an equation! Solutions: r=24.
Graphical form: Equation $\"5%2F2%2Ar%2B5%2F2%2A%28r%2B6%29=135\"$ was fully solved.
Text form: 5/2*r+5/2*(r+6)=135 simplifies to 0=0
Cartoon (animation) form: $\"simplify_cartoon%28+5%2F2%2Ar%2B5%2F2%2A%28r%2B6%29=135+%29\"$
For tutors: simplify_cartoon( 5/2*r+5/2*(r+6)=135 )
If you have a website, here's a link to this solution.

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DETAILED EXPLANATION

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Look at $\"5%2F2%2Ar%2B5%2F2%2A%28r%2B6%29=highlight_red%28+135+%29\"$ .
Moved these terms to the left $\"highlight_green%28+-135+%29\"$
It becomes $\"5%2F2%2Ar%2B5%2F2%2A%28r%2B6%29-highlight_green%28+135+%29=0\"$ .
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Look at $\"5%2F2%2Ar%2Bhighlight_red%28+5%2F2%2A%28r%2B6%29+%29-135=0\"$ .
Expanded term $\"5%2F2\"$ by using associative property on $\"%28r%2B6%29\"$
It becomes $\"5%2F2%2Ar%2Bhighlight_green%28+5%2F2%2Ar+%29%2Bhighlight_green%28+5%2F2%2A6+%29-135=0\"$ .
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Look at $\"5%2F2%2Ar%2B5%2F2%2Ar%2B5%2Fhighlight_red%28+2+%29%2Ahighlight_red%28+6+%29-135=0\"$ .
Factors 6 and 2 have greatest common factor (GCF) of 2. Reducing fraction.
It becomes $\"5%2F2%2Ar%2B5%2F2%2Ar%2B5%2Fhighlight_green%28+1+%29%2Ahighlight_green%28+3+%29-135=0\"$ .
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Look at $\"5%2F2%2Ar%2B5%2F2%2Ar%2Bhighlight_red%28+5+%29%2F1%2Ahighlight_red%28+3+%29-135=0\"$ .
Multiplied numerator integers
It becomes $\"5%2F2%2Ar%2B5%2F2%2Ar%2Bhighlight_green%28+15+%29%2F1-135=0\"$ .
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Look at $\"5%2F2%2Ar%2B5%2F2%2Ar%2Bhighlight_red%28+15%2F1+%29-highlight_red%28+135+%29=0\"$ .
Added fractions or integers together
It becomes $\"5%2F2%2Ar%2B5%2F2%2Ar%2Bhighlight_green%28+-120+%29=0\"$ .
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Look at $\"5%2F2%2Ar%2B5%2F2%2Ar%2Bhighlight_red%28+-120+%29=0\"$ .
Removed extra sign in front of $\"-120\"$
It becomes $\"5%2F2%2Ar%2B5%2F2%2Ar-highlight_green%28+120+%29=0\"$ .
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Look at $\"highlight_red%28+5%2F2%2Ar+%29%2Bhighlight_red%28+5%2F2%2Ar+%29-120=0\"$ .
Eliminated similar terms $\"highlight_red%28+5%2F2%2Ar+%29\"$ , $\"highlight_red%28+5%2F2%2Ar+%29\"$ replacing them with $\"highlight_green%28+%285%2A1%2F2%2B5%2A1%2F2%29%2Ar+%29\"$
It becomes $\"highlight_green%28+%285%2A1%2F2%2B5%2A1%2F2%29%2Ar+%29-120=0\"$ .
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Look at $\"%28highlight_red%28+5+%29%2Ahighlight_red%28+1+%29%2F2%2B5%2A1%2F2%29%2Ar-120=0\"$ .
Multiplied numerator integers
It becomes $\"%28highlight_green%28+5+%29%2F2%2B5%2A1%2F2%29%2Ar-120=0\"$ .
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Look at $\"%285%2F2%2Bhighlight_red%28+5+%29%2Ahighlight_red%28+1+%29%2F2%29%2Ar-120=0\"$ .
Multiplied numerator integers
It becomes $\"%285%2F2%2Bhighlight_green%28+5+%29%2F2%29%2Ar-120=0\"$ .
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Look at $\"%28highlight_red%28+5%2F2+%29%2Bhighlight_red%28+5%2F2+%29%29%2Ar-120=0\"$ .
Added fractions or integers together
It becomes $\"%28highlight_green%28+10%2F2+%29%29%2Ar-120=0\"$ .
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Look at $\"highlight_red%28+%28highlight_red%28+10%2F2+%29%29%2Ar+%29-120=0\"$ .
Remove unneeded parentheses around factor $\"highlight_red%28+10+%29\"$ , $\"highlight_red%28+1%2F2+%29\"$
It becomes $\"highlight_green%28+10+%29%2Fhighlight_green%28+2+%29%2Ar-120=0\"$ .
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Look at $\"highlight_red%28+10+%29%2Fhighlight_red%28+2+%29%2Ar-120=0\"$ .
Factors 10 and 2 have greatest common factor (GCF) of 2. Reducing fraction.
It becomes $\"highlight_green%28+5+%29%2Fhighlight_green%28+1+%29%2Ar-120=0\"$ .
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Look at $\"5%2Fhighlight_red%28+1+%29%2Ar-120=0\"$ .
Remove extraneous '1' from product $\"highlight_red%28+1%2F1+%29\"$
It becomes $\"5%2Ar-120=0\"$ .
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Look at $\"highlight_red%28+5%2Ar-120+%29=0\"$ .
Solved linear equation $\"highlight_red%28+5%2Ar-120=0+%29\"$ equivalent to 5*r-120 =0
It becomes $\"highlight_green%28+0+%29=0\"$ .
Result: $\"0=0\"$
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Universal Simplifier and Solver

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Done!

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