SOLUTION: How do I solve 2(2r-4)/5=3r+6/4-3/2

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Question 33867This question is from textbook
: How do I solve 2(2r-4)/5=3r+6/4-3/2 This question is from textbook

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: r=-0.727272727272727.
  • Graphical form: Equation 2%2A%282r-4%29%2F5=3r%2B6%2F4-3%2F2 was fully solved.
  • Text form: 2*(2r-4)/5=3r+6/4-3/2 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+2%2A%282r-4%29%2F5=3r%2B6%2F4-3%2F2+%29
    For tutors: simplify_cartoon( 2*(2r-4)/5=3r+6/4-3/2 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 2%2A%282%2Ar-4%29%2F5=3%2Ar%2Bhighlight_red%28+6+%29%2Fhighlight_red%28+4+%29-3%2F2.
Factors 6 and 4 have greatest common factor (GCF) of 2. Reducing fraction.
It becomes 2%2A%282%2Ar-4%29%2F5=3%2Ar%2Bhighlight_green%28+3+%29%2Fhighlight_green%28+2+%29-3%2F2.
Look at 2%2A%282%2Ar-4%29%2F5=3%2Ar%2Bhighlight_red%28+3%2F2+%29-highlight_red%28+3%2F2+%29.
Added fractions or integers together
It becomes 2%2A%282%2Ar-4%29%2F5=3%2Ar%2Bhighlight_green%28+0%2F2+%29.
Look at 2%2A%282%2Ar-4%29%2F5=3%2Ar%2Bhighlight_red%28+0+%29%2Fhighlight_red%28+2+%29.
Factors 0 and 2 have greatest common factor (GCF) of 2. Reducing fraction.
It becomes 2%2A%282%2Ar-4%29%2F5=3%2Ar%2Bhighlight_green%28+0+%29%2Fhighlight_green%28+1+%29.
Look at 2%2A%282%2Ar-4%29%2F5=3%2Ar%2Bhighlight_red%28+0%2F1+%29.
Remove extraneous zero highlight_red%28+0%2F1+%29
It becomes 2%2A%282%2Ar-4%29%2F5=3%2Ar.
Look at 2%2A%282%2Ar-4%29%2F5=highlight_red%28+3%2Ar+%29.
Moved these terms to the left highlight_green%28+-3%2Ar+%29
It becomes 2%2A%282%2Ar-4%29%2F5-highlight_green%28+3%2Ar+%29=0.
Look at highlight_red%28+2%2A%282%2Ar-4%29%2F5+%29-3%2Ar=0.
Expanded term 2%2F5 by using associative property on %282%2Ar-4%29
It becomes highlight_green%28+2%2F5%2A2%2Ar+%29-highlight_green%28+2%2F5%2A4+%29-3%2Ar=0.
Look at highlight_red%28+2+%29%2F5%2Ahighlight_red%28+2+%29%2Ar-2%2F5%2A4-3%2Ar=0.
Multiplied numerator integers
It becomes highlight_green%28+4+%29%2F5%2Ar-2%2F5%2A4-3%2Ar=0.
Look at 4%2F5%2Ar-highlight_red%28+2+%29%2F5%2Ahighlight_red%28+4+%29-3%2Ar=0.
Multiplied numerator integers
It becomes 4%2F5%2Ar-highlight_green%28+8+%29%2F5-3%2Ar=0.
Look at 4%2F5%2Ar-highlight_red%28+8%2F5+%29-3%2Ar=0.
Moved -8%2F5 to the right of expression
It becomes 4%2F5%2Ar-3%2Ar-highlight_green%28+8%2F5+%29=0.
Look at highlight_red%28+4%2F5%2Ar+%29-highlight_red%28+3%2Ar+%29-8%2F5=0.
Eliminated similar terms highlight_red%28+4%2F5%2Ar+%29,highlight_red%28+-3%2Ar+%29 replacing them with highlight_green%28+%284%2A1%2F5-3%29%2Ar+%29
It becomes highlight_green%28+%284%2A1%2F5-3%29%2Ar+%29-8%2F5=0.
Look at %28highlight_red%28+4+%29%2Ahighlight_red%28+1+%29%2F5-3%29%2Ar-8%2F5=0.
Multiplied numerator integers
It becomes %28highlight_green%28+4+%29%2F5-3%29%2Ar-8%2F5=0.
Look at %28highlight_red%28+4%2F5+%29-highlight_red%28+3+%29%29%2Ar-8%2F5=0.
Added fractions or integers together
It becomes %28-highlight_green%28+11%2F5+%29%29%2Ar-8%2F5=0.
Look at highlight_red%28+%28-highlight_red%28+11%2F5+%29%29%2Ar+%29-8%2F5=0.
Remove unneeded parentheses around factor highlight_red%28+11+%29,highlight_red%28+1%2F5+%29
It becomes -highlight_green%28+11+%29%2Fhighlight_green%28+5+%29%2Ar-8%2F5=0.
Look at highlight_red%28+-11%2F5%2Ar-8%2F5+%29=0.
Solved linear equation highlight_red%28+-11%2F5%2Ar-8%2F5=0+%29 equivalent to -2.2*r-1.6 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: r=-0.727272727272727.

Universal Simplifier and Solver


Done!