SOLUTION: Solve for X 2/3*(x-6)-4=3/4*(x+2)

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Question 6284: Solve for X
2/3*(x-6)-4=3/4*(x+2)
Answer by ichudov(507) 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


  • 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.

DETAILED EXPLANATION

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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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
This is an equation! Solutions: x=-114.

Universal Simplifier and Solver


Done!