document.write( "Question 34040: -(x+6)+4x=3(x-1)+7 \n" ); document.write( "

Algebra.Com's Answer #20391 by ichudov(507) $\"\"$ $\"About$

You can put this solution on YOUR website!
This equation has no solutions. It simplifies to 0=10. \r
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Solved by pluggable solver: EXPLAIN simplification of an expression

Your Result:

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Graphical form: $\"-%28x%2B6%29%2B4x=3%2A%28x-1%29%2B7\"$ simplifies to $\"-10=0\"$
Text form: -(x+6)+4x=3*(x-1)+7 simplifies to -10=0
Cartoon (animation) form: $\"simplify_cartoon%28+-%28x%2B6%29%2B4x=3%2A%28x-1%29%2B7+%29\"$
For tutors: simplify_cartoon( -(x+6)+4x=3*(x-1)+7 )
If you have a website, here's a link to this solution.

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DETAILED EXPLANATION

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Look at $\"-highlight_red%28+%28x%2B6%29+%29%2B4%2Ax=3%2A%28x-1%29%2B7\"$ .
Remove unneeded parentheses around terms $\"highlight_red%28+-x+%29\"$ , $\"highlight_red%28+-6+%29\"$
It becomes $\"-highlight_green%28+x+%29-highlight_green%28+6+%29%2B4%2Ax=3%2A%28x-1%29%2B7\"$ .
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Look at $\"-x-highlight_red%28+6+%29%2B4%2Ax=3%2A%28x-1%29%2B7\"$ .
Moved $\"-6\"$ to the right of expression
It becomes $\"-x%2B4%2Ax-highlight_green%28+6+%29=3%2A%28x-1%29%2B7\"$ .
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Look at $\"-highlight_red%28+x+%29%2Bhighlight_red%28+4%2Ax+%29-6=3%2A%28x-1%29%2B7\"$ .
Eliminated similar terms $\"highlight_red%28+-x+%29\"$ , $\"highlight_red%28+4%2Ax+%29\"$ replacing them with $\"highlight_green%28+%28-1%2B4%29%2Ax+%29\"$
It becomes $\"highlight_green%28+%28-1%2B4%29%2Ax+%29-6=3%2A%28x-1%29%2B7\"$ .
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Look at $\"%28-highlight_red%28+1+%29%2Bhighlight_red%28+4+%29%29%2Ax-6=3%2A%28x-1%29%2B7\"$ .
Added fractions or integers together
It becomes $\"%28highlight_green%28+3+%29%29%2Ax-6=3%2A%28x-1%29%2B7\"$ .
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Look at $\"highlight_red%28+%28highlight_red%28+3+%29%29%2Ax+%29-6=3%2A%28x-1%29%2B7\"$ .
Remove unneeded parentheses around factor $\"highlight_red%28+3+%29\"$
It becomes $\"highlight_green%28+3+%29%2Ax-6=3%2A%28x-1%29%2B7\"$ .
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Look at $\"3%2Ax-6=highlight_red%28+3%2A%28x-1%29%2B7+%29\"$ .
Moved these terms to the left $\"highlight_green%28+-3%2A%28x-1%29+%29\"$ , $\"highlight_green%28+-7+%29\"$
It becomes $\"3%2Ax-6-highlight_green%28+3%2A%28x-1%29+%29-highlight_green%28+7+%29=0\"$ .
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Look at $\"3%2Ax-highlight_red%28+6+%29-3%2A%28x-1%29-highlight_red%28+7+%29=0\"$ .
Added fractions or integers together
It becomes $\"3%2Ax%2Bhighlight_green%28+-13+%29-3%2A%28x-1%29=0\"$ .
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Look at $\"3%2Ax%2Bhighlight_red%28+-13+%29-3%2A%28x-1%29=0\"$ .
Moved $\"-13\"$ to the right of expression
It becomes $\"3%2Ax-3%2A%28x-1%29%2Bhighlight_green%28+-13+%29=0\"$ .
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Look at $\"3%2Ax-3%2A%28x-1%29%2Bhighlight_red%28+-13+%29=0\"$ .
Removed extra sign in front of $\"-13\"$
It becomes $\"3%2Ax-3%2A%28x-1%29-highlight_green%28+13+%29=0\"$ .
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Look at $\"3%2Ax-highlight_red%28+3%2A%28x-1%29+%29-13=0\"$ .
Expanded term $\"-3\"$ by using associative property on $\"%28x-1%29\"$
It becomes $\"3%2Ax-highlight_green%28+3%2Ax+%29%2Bhighlight_green%28+3%2A1+%29-13=0\"$ .
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Look at $\"3%2Ax-3%2Ax%2Bhighlight_red%28+3+%29%2Ahighlight_red%28+1+%29-13=0\"$ .
Multiplied numerator integers
It becomes $\"3%2Ax-3%2Ax%2Bhighlight_green%28+3+%29-13=0\"$ .
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Look at $\"3%2Ax-3%2Ax%2Bhighlight_red%28+3+%29-highlight_red%28+13+%29=0\"$ .
Added fractions or integers together
It becomes $\"3%2Ax-3%2Ax%2Bhighlight_green%28+-10+%29=0\"$ .
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Look at $\"3%2Ax-3%2Ax%2Bhighlight_red%28+-10+%29=0\"$ .
Removed extra sign in front of $\"-10\"$
It becomes $\"3%2Ax-3%2Ax-highlight_green%28+10+%29=0\"$ .
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Look at $\"highlight_red%28+3%2Ax+%29-highlight_red%28+3%2Ax+%29-10=0\"$ .
Eliminated similar terms $\"highlight_red%28+3%2Ax+%29\"$ , $\"highlight_red%28+-3%2Ax+%29\"$ replacing them with $\"highlight_green%28+%283-3%29%2Ax+%29\"$
It becomes $\"highlight_green%28+%283-3%29%2Ax+%29-10=0\"$ .
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Look at $\"highlight_red%28+%283-3%29%2Ax+%29-10=0\"$ .
Since $\"highlight_red%28+%283-3%29%2Ax+%29\"$ has zero as a factor, it should be replaced with a zero
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Look at $\"0-10=0\"$ .
Added fractions or integers together
It becomes $\"0-10=0\"$ .
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Look at $\"highlight_red%28+0+%29-10=0\"$ .
Remove extraneous zero $\"highlight_red%28+0+%29\"$
It becomes $\"-10=0\"$ .
Result: $\"-10=0\"$
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Universal Simplifier and Solver

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Done!

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