document.write( "Question 941487: solve the equation below and show steps in work\r
\n" ); document.write( "\n" ); document.write( "1/3(12+x)=-8(6-x) \n" ); document.write( "

Algebra.Com's Answer #573895 by srinivas.g(540) $\"\"$ $\"About$

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=6.78260869565217.
Graphical form: Equation $\"%281%2F3%29%2A%2812%2Bx%29=-8%2A%286-x%29\"$ was fully solved.
Text form: (1/3)*(12+x)=-8*(6-x) simplifies to 0=0
Cartoon (animation) form: $\"simplify_cartoon%28+%281%2F3%29%2A%2812%2Bx%29=-8%2A%286-x%29+%29\"$
For tutors: simplify_cartoon( (1/3)*(12+x)=-8*(6-x) )
If you have a website, here's a link to this solution.

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DETAILED EXPLANATION

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Look at $\"highlight_red%28+%28highlight_red%28+1%2F3+%29%29%2A%2812%2Bx%29+%29=-8%2A%286-x%29\"$ .
Remove unneeded parentheses around factor $\"highlight_red%28+1+%29\"$ , $\"highlight_red%28+1%2F3+%29\"$
It becomes $\"highlight_green%28+1+%29%2Fhighlight_green%28+3+%29%2A%2812%2Bx%29=-8%2A%286-x%29\"$ .
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Look at $\"highlight_red%28+1+%29%2F3%2A%2812%2Bx%29=-8%2A%286-x%29\"$ .
Remove extraneous '1' from product $\"highlight_red%28+1+%29\"$
It becomes $\"%2812%2Bx%29%2F3=-8%2A%286-x%29\"$ .
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Look at $\"%28highlight_red%28+12+%29%2Bx%29%2F3=-8%2A%286-x%29\"$ .
Moved $\"12\"$ to the right of expression
It becomes $\"%28x%2Bhighlight_green%28+12+%29%29%2F3=-8%2A%286-x%29\"$ .
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Look at $\"%28x%2B12%29%2F3=-8%2A%28highlight_red%28+6+%29-x%29\"$ .
Moved $\"6\"$ to the right of expression
It becomes $\"%28x%2B12%29%2F3=-8%2A%28-x%2Bhighlight_green%28+6+%29%29\"$ .
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Look at $\"%28x%2B12%29%2F3=highlight_red%28+-8%2A%28-x%2B6%29+%29\"$ .
Moved these terms to the left $\"highlight_green%28+8%2A%28-x%2B6%29+%29\"$
It becomes $\"%28x%2B12%29%2F3%2Bhighlight_green%28+8%2A%28-x%2B6%29+%29=0\"$ .
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Look at $\"highlight_red%28+%28x%2B12%29%2F3+%29%2B8%2A%28-x%2B6%29=0\"$ .
Expanded term $\"1%2F3\"$ by using associative property on $\"%28x%2B12%29\"$
It becomes $\"highlight_green%28+1%2F3%2Ax+%29%2Bhighlight_green%28+1%2F3%2A12+%29%2B8%2A%28-x%2B6%29=0\"$ .
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Look at $\"highlight_red%28+1+%29%2F3%2Ax%2B1%2F3%2A12%2B8%2A%28-x%2B6%29=0\"$ .
Remove extraneous '1' from product $\"highlight_red%28+1+%29\"$
It becomes $\"x%2F3%2B1%2F3%2A12%2B8%2A%28-x%2B6%29=0\"$ .
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Look at $\"x%2F3%2B1%2Fhighlight_red%28+3+%29%2Ahighlight_red%28+12+%29%2B8%2A%28-x%2B6%29=0\"$ .
Factors 12 and 3 have greatest common factor (GCF) of 3. Reducing fraction.
It becomes $\"x%2F3%2B1%2Fhighlight_green%28+1+%29%2Ahighlight_green%28+4+%29%2B8%2A%28-x%2B6%29=0\"$ .
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Look at $\"x%2F3%2Bhighlight_red%28+1+%29%2F1%2Ahighlight_red%28+4+%29%2B8%2A%28-x%2B6%29=0\"$ .
Multiplied numerator integers
It becomes $\"x%2F3%2Bhighlight_green%28+4+%29%2F1%2B8%2A%28-x%2B6%29=0\"$ .
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Look at $\"x%2F3%2Bhighlight_red%28+4%2F1+%29%2B8%2A%28-x%2B6%29=0\"$ .
Moved $\"4%2F1\"$ to the right of expression
It becomes $\"x%2F3%2B8%2A%28-x%2B6%29%2Bhighlight_green%28+4%2F1+%29=0\"$ .
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Look at $\"x%2F3%2B8%2A%28-x%2B6%29%2B4%2Fhighlight_red%28+1+%29=0\"$ .
Remove extraneous '1' from product $\"highlight_red%28+1%2F1+%29\"$
It becomes $\"x%2F3%2B8%2A%28-x%2B6%29%2B4=0\"$ .
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Look at $\"x%2F3%2Bhighlight_red%28+8%2A%28-x%2B6%29+%29%2B4=0\"$ .
Expanded term $\"8\"$ by using associative property on $\"%28-x%2B6%29\"$
It becomes $\"x%2F3-highlight_green%28+8%2Ax+%29%2Bhighlight_green%28+8%2A6+%29%2B4=0\"$ .
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Look at $\"x%2F3-8%2Ax%2Bhighlight_red%28+8+%29%2Ahighlight_red%28+6+%29%2B4=0\"$ .
Multiplied numerator integers
It becomes $\"x%2F3-8%2Ax%2Bhighlight_green%28+48+%29%2B4=0\"$ .
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Look at $\"x%2F3-8%2Ax%2Bhighlight_red%28+48+%29%2Bhighlight_red%28+4+%29=0\"$ .
Added fractions or integers together
It becomes $\"x%2F3-8%2Ax%2Bhighlight_green%28+52+%29=0\"$ .
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Look at $\"highlight_red%28+x%2F3+%29-highlight_red%28+8%2Ax+%29%2B52=0\"$ .
Eliminated similar terms $\"highlight_red%28+x%2F3+%29\"$ , $\"highlight_red%28+-8%2Ax+%29\"$ replacing them with $\"highlight_green%28+%281%2F3-8%29%2Ax+%29\"$
It becomes $\"highlight_green%28+%281%2F3-8%29%2Ax+%29%2B52=0\"$ .
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Look at $\"%28highlight_red%28+1%2F3+%29-highlight_red%28+8+%29%29%2Ax%2B52=0\"$ .
Added fractions or integers together
It becomes $\"%28-highlight_green%28+23%2F3+%29%29%2Ax%2B52=0\"$ .
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Look at $\"highlight_red%28+%28-highlight_red%28+23%2F3+%29%29%2Ax+%29%2B52=0\"$ .
Remove unneeded parentheses around factor $\"highlight_red%28+23+%29\"$ , $\"highlight_red%28+1%2F3+%29\"$
It becomes $\"-highlight_green%28+23+%29%2Fhighlight_green%28+3+%29%2Ax%2B52=0\"$ .
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Look at $\"highlight_red%28+-23%2F3%2Ax%2B52+%29=0\"$ .
Solved linear equation $\"highlight_red%28+-23%2F3%2Ax%2B52=0+%29\"$ equivalent to -7.66666666666667*x+52 =0
It becomes $\"highlight_green%28+0+%29=0\"$ .
Result: $\"0=0\"$
\n" ); document.write( "This is an equation! Solutions: x=6.78260869565217.

Universal Simplifier and Solver

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Done!

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