SOLUTION: 1/3x-1/6=5/6x+1/12

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Question 22406: 1/3x-1/6=5/6x+1/12
Answer by Alwayscheerful(414) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Here's what you tried:
  • This is an equation! Solutions: x=-0.5.
  • Graphical form: Equation %281%2F3%29%2Ax-1%2F6=%285%2F6%29%2Ax%2B1%2F12 was fully solved.
  • Text form: (1/3)*x-1/6=(5/6)*x+1/12 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+%281%2F3%29%2Ax-1%2F6=%285%2F6%29%2Ax%2B1%2F12+%29
    For tutors: simplify_cartoon( (1/3)*x-1/6=(5/6)*x+1/12 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+%28highlight_red%28+1%2F3+%29%29%2Ax+%29-1%2F6=%285%2F6%29%2Ax%2B1%2F12.
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%2Ax-1%2F6=%285%2F6%29%2Ax%2B1%2F12.
Look at highlight_red%28+1+%29%2F3%2Ax-1%2F6=%285%2F6%29%2Ax%2B1%2F12.
Remove extraneous '1' from product highlight_red%28+1+%29
It becomes x%2F3-1%2F6=%285%2F6%29%2Ax%2B1%2F12.
Look at x%2F3-1%2F6=highlight_red%28+%28highlight_red%28+5%2F6+%29%29%2Ax+%29%2B1%2F12.
Remove unneeded parentheses around factor highlight_red%28+5+%29,highlight_red%28+1%2F6+%29
It becomes x%2F3-1%2F6=highlight_green%28+5+%29%2Fhighlight_green%28+6+%29%2Ax%2B1%2F12.
Look at x%2F3-1%2F6=highlight_red%28+5%2F6%2Ax%2B1%2F12+%29.
Moved these terms to the left highlight_green%28+-5%2F6%2Ax+%29,highlight_green%28+-1%2F12+%29
It becomes x%2F3-1%2F6-highlight_green%28+5%2F6%2Ax+%29-highlight_green%28+1%2F12+%29=0.
Look at x%2F3-highlight_red%28+1%2F6+%29-5%2F6%2Ax-highlight_red%28+1%2F12+%29=0.
Added fractions or integers together
It becomes x%2F3-highlight_green%28+3%2F12+%29-5%2F6%2Ax=0.
Look at x%2F3-highlight_red%28+3%2F12+%29-5%2F6%2Ax=0.
Moved -3%2F12 to the right of expression
It becomes x%2F3-5%2F6%2Ax-highlight_green%28+3%2F12+%29=0.
Look at x%2F3-5%2F6%2Ax-highlight_red%28+3+%29%2Fhighlight_red%28+12+%29=0.
Factors 3 and 12 have greatest common factor (GCF) of 3. Reducing fraction.
It becomes x%2F3-5%2F6%2Ax-highlight_green%28+1+%29%2Fhighlight_green%28+4+%29=0.
Look at highlight_red%28+x%2F3+%29-highlight_red%28+5%2F6%2Ax+%29-1%2F4=0.
Eliminated similar terms highlight_red%28+x%2F3+%29,highlight_red%28+-5%2F6%2Ax+%29 replacing them with highlight_green%28+%281%2F3-5%2A1%2F6%29%2Ax+%29
It becomes highlight_green%28+%281%2F3-5%2A1%2F6%29%2Ax+%29-1%2F4=0.
Look at %281%2F3-highlight_red%28+5+%29%2Ahighlight_red%28+1+%29%2F6%29%2Ax-1%2F4=0.
Multiplied numerator integers
It becomes %281%2F3-highlight_green%28+5+%29%2F6%29%2Ax-1%2F4=0.
Look at %28highlight_red%28+1%2F3+%29-highlight_red%28+5%2F6+%29%29%2Ax-1%2F4=0.
Added fractions or integers together
It becomes %28-highlight_green%28+3%2F6+%29%29%2Ax-1%2F4=0.
Look at highlight_red%28+%28-highlight_red%28+3%2F6+%29%29%2Ax+%29-1%2F4=0.
Remove unneeded parentheses around factor highlight_red%28+3+%29,highlight_red%28+1%2F6+%29
It becomes -highlight_green%28+3+%29%2Fhighlight_green%28+6+%29%2Ax-1%2F4=0.
Look at -highlight_red%28+3+%29%2Fhighlight_red%28+6+%29%2Ax-1%2F4=0.
Factors 3 and 6 have greatest common factor (GCF) of 3. Reducing fraction.
It becomes -highlight_green%28+1+%29%2Fhighlight_green%28+2+%29%2Ax-1%2F4=0.
Look at -highlight_red%28+1+%29%2F2%2Ax-1%2F4=0.
Remove extraneous '1' from product highlight_red%28+1+%29
It becomes -x%2F2-1%2F4=0.
Look at highlight_red%28+-x%2F2-1%2F4+%29=0.
Solved linear equation highlight_red%28+-x%2F2-1%2F4=0+%29 equivalent to -0.5*x-0.25 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=-0.5.

Universal Simplifier and Solver


Done!

Hope this helps!