document.write( "Question 776918: Please help me simplify this question 5(2d+1)+7(5d+3) \n" ); document.write( "

Algebra.Com's Answer #473796 by psbhowmick(878) $\"\"$ $\"About$

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: Equation $\"5%2A%282%2Ad%2B1%29%2B7%2A%285%2Ad%2B3%29=45%2Ad%2B26\"$ was fully solved.
Text form: 5*(2*d+1)+7*(5*d+3)=45*d+26 simplifies to 0=0
Cartoon (animation) form: $\"simplify_cartoon%28+5%2A%282%2Ad%2B1%29%2B7%2A%285%2Ad%2B3%29=45%2Ad%2B26+%29\"$
For tutors: simplify_cartoon( 5*(2*d+1)+7*(5*d+3)=45*d+26 )
If you have a website, here's a link to this solution.

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DETAILED EXPLANATION

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Look at $\"5%2A%282%2Ad%2B1%29%2B7%2A%285%2Ad%2B3%29=highlight_red%28+45%2Ad%2B26+%29\"$ .
Moved these terms to the left $\"highlight_green%28+-45%2Ad+%29\"$ , $\"highlight_green%28+-26+%29\"$
It becomes

.
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Look at $\"highlight_red%28+5%2A%282%2Ad%2B1%29+%29%2B7%2A%285%2Ad%2B3%29-45%2Ad-26=0\"$ .
Expanded term $\"5\"$ by using associative property on $\"%282%2Ad%2B1%29\"$
It becomes

.
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Look at

.
Multiplied numerator integers
It becomes $\"highlight_green%28+10+%29%2Ad%2B5%2A1%2B7%2A%285%2Ad%2B3%29-45%2Ad-26=0\"$ .
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Look at $\"10%2Ad%2Bhighlight_red%28+5+%29%2Ahighlight_red%28+1+%29%2B7%2A%285%2Ad%2B3%29-45%2Ad-26=0\"$ .
Multiplied numerator integers
It becomes $\"10%2Ad%2Bhighlight_green%28+5+%29%2B7%2A%285%2Ad%2B3%29-45%2Ad-26=0\"$ .
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Look at $\"10%2Ad%2Bhighlight_red%28+5+%29%2B7%2A%285%2Ad%2B3%29-45%2Ad-highlight_red%28+26+%29=0\"$ .
Added fractions or integers together
It becomes $\"10%2Ad%2Bhighlight_green%28+-21+%29%2B7%2A%285%2Ad%2B3%29-45%2Ad=0\"$ .
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Look at $\"10%2Ad%2Bhighlight_red%28+-21+%29%2B7%2A%285%2Ad%2B3%29-45%2Ad=0\"$ .
Moved $\"-21\"$ to the right of expression
It becomes $\"10%2Ad%2B7%2A%285%2Ad%2B3%29-45%2Ad%2Bhighlight_green%28+-21+%29=0\"$ .
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Look at $\"10%2Ad%2B7%2A%285%2Ad%2B3%29-45%2Ad%2Bhighlight_red%28+-21+%29=0\"$ .
Removed extra sign in front of $\"-21\"$
It becomes $\"10%2Ad%2B7%2A%285%2Ad%2B3%29-45%2Ad-highlight_green%28+21+%29=0\"$ .
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Look at $\"highlight_red%28+10%2Ad+%29%2B7%2A%285%2Ad%2B3%29-highlight_red%28+45%2Ad+%29-21=0\"$ .
Eliminated similar terms $\"highlight_red%28+10%2Ad+%29\"$ , $\"highlight_red%28+-45%2Ad+%29\"$ replacing them with $\"highlight_green%28+%2810-45%29%2Ad+%29\"$
It becomes $\"highlight_green%28+%2810-45%29%2Ad+%29%2B7%2A%285%2Ad%2B3%29-21=0\"$ .
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Look at $\"%28highlight_red%28+10+%29-highlight_red%28+45+%29%29%2Ad%2B7%2A%285%2Ad%2B3%29-21=0\"$ .
Added fractions or integers together
It becomes $\"%28highlight_green%28+-35+%29%29%2Ad%2B7%2A%285%2Ad%2B3%29-21=0\"$ .
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Look at $\"%28highlight_red%28+-35+%29%29%2Ad%2B7%2A%285%2Ad%2B3%29-21=0\"$ .
Removed extra sign in front of $\"-35\"$
It becomes $\"%28-highlight_green%28+35+%29%29%2Ad%2B7%2A%285%2Ad%2B3%29-21=0\"$ .
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Look at $\"highlight_red%28+%28-highlight_red%28+35+%29%29%2Ad+%29%2B7%2A%285%2Ad%2B3%29-21=0\"$ .
Remove unneeded parentheses around factor $\"highlight_red%28+35+%29\"$
It becomes $\"-highlight_green%28+35+%29%2Ad%2B7%2A%285%2Ad%2B3%29-21=0\"$ .
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Look at $\"-35%2Ad%2Bhighlight_red%28+7%2A%285%2Ad%2B3%29+%29-21=0\"$ .
Expanded term $\"7\"$ by using associative property on $\"%285%2Ad%2B3%29\"$
It becomes $\"-35%2Ad%2Bhighlight_green%28+7%2A5%2Ad+%29%2Bhighlight_green%28+7%2A3+%29-21=0\"$ .
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Look at $\"-35%2Ad%2Bhighlight_red%28+7+%29%2Ahighlight_red%28+5+%29%2Ad%2B7%2A3-21=0\"$ .
Multiplied numerator integers
It becomes $\"-35%2Ad%2Bhighlight_green%28+35+%29%2Ad%2B7%2A3-21=0\"$ .
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Look at $\"-35%2Ad%2B35%2Ad%2Bhighlight_red%28+7+%29%2Ahighlight_red%28+3+%29-21=0\"$ .
Multiplied numerator integers
It becomes $\"-35%2Ad%2B35%2Ad%2Bhighlight_green%28+21+%29-21=0\"$ .
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Look at $\"-35%2Ad%2B35%2Ad%2Bhighlight_red%28+21+%29-highlight_red%28+21+%29=0\"$ .
Added fractions or integers together
It becomes $\"-35%2Ad%2B35%2Ad%2Bhighlight_green%28+0+%29=0\"$ .
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Look at $\"-35%2Ad%2B35%2Ad%2Bhighlight_red%28+0+%29=0\"$ .
Remove extraneous zero $\"highlight_red%28+0+%29\"$
It becomes $\"-35%2Ad%2B35%2Ad=0\"$ .
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Look at $\"-highlight_red%28+35%2Ad+%29%2Bhighlight_red%28+35%2Ad+%29=0\"$ .
Eliminated similar terms $\"highlight_red%28+-35%2Ad+%29\"$ , $\"highlight_red%28+35%2Ad+%29\"$ replacing them with $\"highlight_green%28+%28-35%2B35%29%2Ad+%29\"$
It becomes $\"highlight_green%28+%28-35%2B35%29%2Ad+%29=0\"$ .
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Look at $\"highlight_red%28+%28-35%2B35%29%2Ad+%29=0\"$ .
Since $\"highlight_red%28+%28-35%2B35%29%2Ad+%29\"$ 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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