document.write( "Question 6284: Solve for X
\n" ); document.write( "2/3*(x-6)-4=3/4*(x+2) \n" ); document.write( "

Algebra.Com's Answer #3358 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: x=-114.
Graphical form: Equation $\"2%2F3%2A%28x-6%29-4=3%2F4%2A%28x%2B2%29\"$ was fully solved.
Text form: 2/3*(x-6)-4=3/4*(x+2) simplifies to 0=0
Cartoon (animation) form: $\"simplify_cartoon%28+2%2F3%2A%28x-6%29-4=3%2F4%2A%28x%2B2%29+%29\"$
For tutors: simplify_cartoon( 2/3*(x-6)-4=3/4*(x+2) )
If you have a website, here's a link to this solution.

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DETAILED EXPLANATION

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Look at $\"2%2F3%2A%28x-6%29-4=highlight_red%28+3%2F4%2A%28x%2B2%29+%29\"$ .
Moved these terms to the left $\"highlight_green%28+-3%2F4%2A%28x%2B2%29+%29\"$
It becomes $\"2%2F3%2A%28x-6%29-4-highlight_green%28+3%2F4%2A%28x%2B2%29+%29=0\"$ .
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Look at $\"2%2F3%2A%28x-6%29-highlight_red%28+4+%29-3%2F4%2A%28x%2B2%29=0\"$ .
Moved $\"-4\"$ to the right of expression
It becomes $\"2%2F3%2A%28x-6%29-3%2F4%2A%28x%2B2%29-highlight_green%28+4+%29=0\"$ .
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Look at $\"highlight_red%28+2%2F3%2A%28x-6%29+%29-3%2F4%2A%28x%2B2%29-4=0\"$ .
Expanded term $\"2%2F3\"$ by using associative property on $\"%28x-6%29\"$
It becomes $\"highlight_green%28+2%2F3%2Ax+%29-highlight_green%28+2%2F3%2A6+%29-3%2F4%2A%28x%2B2%29-4=0\"$ .
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Look at $\"2%2F3%2Ax-2%2Fhighlight_red%28+3+%29%2Ahighlight_red%28+6+%29-3%2F4%2A%28x%2B2%29-4=0\"$ .
Factors 6 and 3 have greatest common factor (GCF) of 3. Reducing fraction.
It becomes $\"2%2F3%2Ax-2%2Fhighlight_green%28+1+%29%2Ahighlight_green%28+2+%29-3%2F4%2A%28x%2B2%29-4=0\"$ .
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Look at $\"2%2F3%2Ax-highlight_red%28+2+%29%2F1%2Ahighlight_red%28+2+%29-3%2F4%2A%28x%2B2%29-4=0\"$ .
Multiplied numerator integers
It becomes $\"2%2F3%2Ax-highlight_green%28+4+%29%2F1-3%2F4%2A%28x%2B2%29-4=0\"$ .
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Look at $\"2%2F3%2Ax-highlight_red%28+4%2F1+%29-3%2F4%2A%28x%2B2%29-highlight_red%28+4+%29=0\"$ .
Added fractions or integers together
It becomes $\"2%2F3%2Ax%2Bhighlight_green%28+-8+%29-3%2F4%2A%28x%2B2%29=0\"$ .
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Look at $\"2%2F3%2Ax%2Bhighlight_red%28+-8+%29-3%2F4%2A%28x%2B2%29=0\"$ .
Moved $\"-8\"$ to the right of expression
It becomes $\"2%2F3%2Ax-3%2F4%2A%28x%2B2%29%2Bhighlight_green%28+-8+%29=0\"$ .
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Look at $\"2%2F3%2Ax-3%2F4%2A%28x%2B2%29%2Bhighlight_red%28+-8+%29=0\"$ .
Removed extra sign in front of $\"-8\"$
It becomes $\"2%2F3%2Ax-3%2F4%2A%28x%2B2%29-highlight_green%28+8+%29=0\"$ .
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Look at $\"2%2F3%2Ax-highlight_red%28+3%2F4%2A%28x%2B2%29+%29-8=0\"$ .
Expanded term $\"-3%2F4\"$ by using associative property on $\"%28x%2B2%29\"$
It becomes $\"2%2F3%2Ax-highlight_green%28+3%2F4%2Ax+%29-highlight_green%28+3%2F4%2A2+%29-8=0\"$ .
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Look at $\"2%2F3%2Ax-3%2F4%2Ax-3%2Fhighlight_red%28+4+%29%2Ahighlight_red%28+2+%29-8=0\"$ .
Factors 2 and 4 have greatest common factor (GCF) of 2. Reducing fraction.
It becomes $\"2%2F3%2Ax-3%2F4%2Ax-3%2Fhighlight_green%28+2+%29%2Ahighlight_green%28+1+%29-8=0\"$ .
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Look at $\"2%2F3%2Ax-3%2F4%2Ax-highlight_red%28+3+%29%2F2%2Ahighlight_red%28+1+%29-8=0\"$ .
Multiplied numerator integers
It becomes $\"2%2F3%2Ax-3%2F4%2Ax-highlight_green%28+3+%29%2F2-8=0\"$ .
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Look at $\"2%2F3%2Ax-3%2F4%2Ax-highlight_red%28+3%2F2+%29-highlight_red%28+8+%29=0\"$ .
Added fractions or integers together
It becomes $\"2%2F3%2Ax-3%2F4%2Ax-highlight_green%28+19%2F2+%29=0\"$ .
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Look at $\"highlight_red%28+2%2F3%2Ax+%29-highlight_red%28+3%2F4%2Ax+%29-19%2F2=0\"$ .
Eliminated similar terms $\"highlight_red%28+2%2F3%2Ax+%29\"$ , $\"highlight_red%28+-3%2F4%2Ax+%29\"$ replacing them with $\"highlight_green%28+%282%2A1%2F3-3%2A1%2F4%29%2Ax+%29\"$
It becomes $\"highlight_green%28+%282%2A1%2F3-3%2A1%2F4%29%2Ax+%29-19%2F2=0\"$ .
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Look at $\"%28highlight_red%28+2+%29%2Ahighlight_red%28+1+%29%2F3-3%2A1%2F4%29%2Ax-19%2F2=0\"$ .
Multiplied numerator integers
It becomes $\"%28highlight_green%28+2+%29%2F3-3%2A1%2F4%29%2Ax-19%2F2=0\"$ .
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Look at $\"%282%2F3-highlight_red%28+3+%29%2Ahighlight_red%28+1+%29%2F4%29%2Ax-19%2F2=0\"$ .
Multiplied numerator integers
It becomes $\"%282%2F3-highlight_green%28+3+%29%2F4%29%2Ax-19%2F2=0\"$ .
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Look at $\"%28highlight_red%28+2%2F3+%29-highlight_red%28+3%2F4+%29%29%2Ax-19%2F2=0\"$ .
Added fractions or integers together
It becomes $\"%28-highlight_green%28+1%2F12+%29%29%2Ax-19%2F2=0\"$ .
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Look at $\"highlight_red%28+%28-highlight_red%28+1%2F12+%29%29%2Ax+%29-19%2F2=0\"$ .
Remove unneeded parentheses around factor $\"highlight_red%28+1+%29\"$ , $\"highlight_red%28+1%2F12+%29\"$
It becomes $\"-highlight_green%28+1+%29%2Fhighlight_green%28+12+%29%2Ax-19%2F2=0\"$ .
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Look at $\"-highlight_red%28+1+%29%2F12%2Ax-19%2F2=0\"$ .
Remove extraneous '1' from product $\"highlight_red%28+1+%29\"$
It becomes $\"-x%2F12-19%2F2=0\"$ .
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Look at $\"highlight_red%28+-x%2F12-19%2F2+%29=0\"$ .
Solved linear equation $\"highlight_red%28+-x%2F12-19%2F2=0+%29\"$ equivalent to -0.0833333333333333*x-9.5 =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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