document.write( "Question 6772: how do you solve:\r
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Algebra.Com's Answer #3730 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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Graphical form: $\"3%2F4%2A%285x%2B6y%29%2A17%2B85%2F2%2B4x-2y\"$ simplifies to $\"271%2F4%2Ax%2B149%2F2%2Ay%2B85%2F2\"$
Text form: 3/4*(5x+6y)*17+85/2+4x-2y simplifies to 271/4*x+149/2*y+85/2
Cartoon (animation) form: $\"simplify_cartoon%28+3%2F4%2A%285x%2B6y%29%2A17%2B85%2F2%2B4x-2y+%29\"$
For tutors: simplify_cartoon( 3/4*(5x+6y)*17+85/2+4x-2y )
If you have a website, here's a link to this solution.

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DETAILED EXPLANATION

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Look at

.
Multiplied numerator integers
It becomes $\"highlight_green%28+51+%29%2F4%2A%285%2Ax%2B6%2Ay%29%2B85%2F2%2B4%2Ax-2%2Ay\"$ .
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Look at $\"51%2F4%2A%285%2Ax%2B6%2Ay%29%2Bhighlight_red%28+85%2F2+%29%2B4%2Ax-2%2Ay\"$ .
Moved $\"85%2F2\"$ to the right of expression
It becomes $\"51%2F4%2A%285%2Ax%2B6%2Ay%29%2B4%2Ax-2%2Ay%2Bhighlight_green%28+85%2F2+%29\"$ .
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Look at $\"highlight_red%28+51%2F4%2A%285%2Ax%2B6%2Ay%29+%29%2B4%2Ax-2%2Ay%2B85%2F2\"$ .
Expanded term $\"51%2F4\"$ by using associative property on $\"%285%2Ax%2B6%2Ay%29\"$
It becomes

.
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Look at

.
Multiplied numerator integers
It becomes $\"highlight_green%28+255+%29%2F4%2Ax%2B51%2F4%2A6%2Ay%2B4%2Ax-2%2Ay%2B85%2F2\"$ .
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Look at

.
Factors 6 and 4 have greatest common factor (GCF) of 2. Reducing fraction.
It becomes

.
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Look at

.
Multiplied numerator integers
It becomes $\"255%2F4%2Ax%2Bhighlight_green%28+153+%29%2F2%2Ay%2B4%2Ax-2%2Ay%2B85%2F2\"$ .
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Look at $\"highlight_red%28+255%2F4%2Ax+%29%2B153%2F2%2Ay%2Bhighlight_red%28+4%2Ax+%29-2%2Ay%2B85%2F2\"$ .
Eliminated similar terms $\"highlight_red%28+255%2F4%2Ax+%29\"$ , $\"highlight_red%28+4%2Ax+%29\"$ replacing them with $\"highlight_green%28+%28255%2A1%2F4%2B4%29%2Ax+%29\"$
It becomes $\"highlight_green%28+%28255%2A1%2F4%2B4%29%2Ax+%29%2B153%2F2%2Ay-2%2Ay%2B85%2F2\"$ .
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Look at

.
Eliminated similar terms $\"highlight_red%28+153%2F2%2Ay+%29\"$ , $\"highlight_red%28+-2%2Ay+%29\"$ replacing them with $\"highlight_green%28+%28153%2A1%2F2-2%29%2Ay+%29\"$
It becomes $\"%28255%2A1%2F4%2B4%29%2Ax%2Bhighlight_green%28+%28153%2A1%2F2-2%29%2Ay+%29%2B85%2F2\"$ .
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Look at

.
Multiplied numerator integers
It becomes $\"%28highlight_green%28+255+%29%2F4%2B4%29%2Ax%2B%28153%2A1%2F2-2%29%2Ay%2B85%2F2\"$ .
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Look at

.
Added fractions or integers together
It becomes $\"%28highlight_green%28+271%2F4+%29%29%2Ax%2B%28153%2A1%2F2-2%29%2Ay%2B85%2F2\"$ .
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Look at

.
Multiplied numerator integers
It becomes $\"%28271%2F4%29%2Ax%2B%28highlight_green%28+153+%29%2F2-2%29%2Ay%2B85%2F2\"$ .
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Look at $\"%28271%2F4%29%2Ax%2B%28highlight_red%28+153%2F2+%29-highlight_red%28+2+%29%29%2Ay%2B85%2F2\"$ .
Added fractions or integers together
It becomes $\"%28271%2F4%29%2Ax%2B%28highlight_green%28+149%2F2+%29%29%2Ay%2B85%2F2\"$ .
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Look at $\"highlight_red%28+%28highlight_red%28+271%2F4+%29%29%2Ax+%29%2B%28149%2F2%29%2Ay%2B85%2F2\"$ .
Remove unneeded parentheses around factor $\"highlight_red%28+271+%29\"$ , $\"highlight_red%28+1%2F4+%29\"$
It becomes $\"highlight_green%28+271+%29%2Fhighlight_green%28+4+%29%2Ax%2B%28149%2F2%29%2Ay%2B85%2F2\"$ .
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Look at $\"271%2F4%2Ax%2Bhighlight_red%28+%28highlight_red%28+149%2F2+%29%29%2Ay+%29%2B85%2F2\"$ .
Remove unneeded parentheses around factor $\"highlight_red%28+149+%29\"$ , $\"highlight_red%28+1%2F2+%29\"$
It becomes $\"271%2F4%2Ax%2Bhighlight_green%28+149+%29%2Fhighlight_green%28+2+%29%2Ay%2B85%2F2\"$ .
Result: $\"271%2F4%2Ax%2B149%2F2%2Ay%2B85%2F2\"$
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Universal Simplifier and Solver

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Done!

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