SOLUTION: {{{ 5/2*r+5/2*(r+6)=135 }}}

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Question 216532: +5%2F2%2Ar%2B5%2F2%2A%28r%2B6%29=135+
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=24.
  • Graphical form: Equation 5%2F2%2Ar%2B5%2F2%2A%28r%2B6%29=135 was fully solved.
  • Text form: 5/2*r+5/2*(r+6)=135 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+5%2F2%2Ar%2B5%2F2%2A%28r%2B6%29=135+%29
    For tutors: simplify_cartoon( 5/2*r+5/2*(r+6)=135 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 5%2F2%2Ar%2B5%2F2%2A%28r%2B6%29=highlight_red%28+135+%29.
Moved these terms to the left highlight_green%28+-135+%29
It becomes 5%2F2%2Ar%2B5%2F2%2A%28r%2B6%29-highlight_green%28+135+%29=0.
Look at 5%2F2%2Ar%2Bhighlight_red%28+5%2F2%2A%28r%2B6%29+%29-135=0.
Expanded term 5%2F2 by using associative property on %28r%2B6%29
It becomes 5%2F2%2Ar%2Bhighlight_green%28+5%2F2%2Ar+%29%2Bhighlight_green%28+5%2F2%2A6+%29-135=0.
Look at 5%2F2%2Ar%2B5%2F2%2Ar%2B5%2Fhighlight_red%28+2+%29%2Ahighlight_red%28+6+%29-135=0.
Factors 6 and 2 have greatest common factor (GCF) of 2. Reducing fraction.
It becomes 5%2F2%2Ar%2B5%2F2%2Ar%2B5%2Fhighlight_green%28+1+%29%2Ahighlight_green%28+3+%29-135=0.
Look at 5%2F2%2Ar%2B5%2F2%2Ar%2Bhighlight_red%28+5+%29%2F1%2Ahighlight_red%28+3+%29-135=0.
Multiplied numerator integers
It becomes 5%2F2%2Ar%2B5%2F2%2Ar%2Bhighlight_green%28+15+%29%2F1-135=0.
Look at 5%2F2%2Ar%2B5%2F2%2Ar%2Bhighlight_red%28+15%2F1+%29-highlight_red%28+135+%29=0.
Added fractions or integers together
It becomes 5%2F2%2Ar%2B5%2F2%2Ar%2Bhighlight_green%28+-120+%29=0.
Look at 5%2F2%2Ar%2B5%2F2%2Ar%2Bhighlight_red%28+-120+%29=0.
Removed extra sign in front of -120
It becomes 5%2F2%2Ar%2B5%2F2%2Ar-highlight_green%28+120+%29=0.
Look at highlight_red%28+5%2F2%2Ar+%29%2Bhighlight_red%28+5%2F2%2Ar+%29-120=0.
Eliminated similar terms highlight_red%28+5%2F2%2Ar+%29,highlight_red%28+5%2F2%2Ar+%29 replacing them with highlight_green%28+%285%2A1%2F2%2B5%2A1%2F2%29%2Ar+%29
It becomes highlight_green%28+%285%2A1%2F2%2B5%2A1%2F2%29%2Ar+%29-120=0.
Look at %28highlight_red%28+5+%29%2Ahighlight_red%28+1+%29%2F2%2B5%2A1%2F2%29%2Ar-120=0.
Multiplied numerator integers
It becomes %28highlight_green%28+5+%29%2F2%2B5%2A1%2F2%29%2Ar-120=0.
Look at %285%2F2%2Bhighlight_red%28+5+%29%2Ahighlight_red%28+1+%29%2F2%29%2Ar-120=0.
Multiplied numerator integers
It becomes %285%2F2%2Bhighlight_green%28+5+%29%2F2%29%2Ar-120=0.
Look at %28highlight_red%28+5%2F2+%29%2Bhighlight_red%28+5%2F2+%29%29%2Ar-120=0.
Added fractions or integers together
It becomes %28highlight_green%28+10%2F2+%29%29%2Ar-120=0.
Look at highlight_red%28+%28highlight_red%28+10%2F2+%29%29%2Ar+%29-120=0.
Remove unneeded parentheses around factor highlight_red%28+10+%29,highlight_red%28+1%2F2+%29
It becomes highlight_green%28+10+%29%2Fhighlight_green%28+2+%29%2Ar-120=0.
Look at highlight_red%28+10+%29%2Fhighlight_red%28+2+%29%2Ar-120=0.
Factors 10 and 2 have greatest common factor (GCF) of 2. Reducing fraction.
It becomes highlight_green%28+5+%29%2Fhighlight_green%28+1+%29%2Ar-120=0.
Look at 5%2Fhighlight_red%28+1+%29%2Ar-120=0.
Remove extraneous '1' from product highlight_red%28+1%2F1+%29
It becomes 5%2Ar-120=0.
Look at highlight_red%28+5%2Ar-120+%29=0.
Solved linear equation highlight_red%28+5%2Ar-120=0+%29 equivalent to 5*r-120 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: r=24.

Universal Simplifier and Solver


Done!