SOLUTION: solve each equation. 2/y+ 5/2 = 4 - 2/3y

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Question 932162: solve each equation.
2/y+ 5/2 = 4 - 2/3y
Found 2 solutions by srinivas.g, MathTherapy:
Answer by srinivas.g(540) About Me  (Show Source):
You can put this solution on YOUR website!
+2%2Fy++%2B5%2F2+=4+-2%2F%283y%29
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Graphical form: %282%2Fy%29%2B%285%2F2%29=4-2%2F%283y%29 simplifies to 8%2F3%2Fy-3%2F2=0
  • Text form: (2/y)+(5/2)=4-2/(3y) simplifies to 8/3/y-3/2=0
  • Cartoon (animation) form: simplify_cartoon%28+%282%2Fy%29%2B%285%2F2%29=4-2%2F%283y%29+%29
    For tutors: simplify_cartoon( (2/y)+(5/2)=4-2/(3y) )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+%282%2Fy%29+%29%2B%285%2F2%29=4-2%2F%283y%29.
Remove unneeded parentheses around terms highlight_red%28+2%2Fy+%29
It becomes highlight_green%28+2%2Fy+%29%2B%285%2F2%29=4-2%2F%283y%29.
Look at 2%2Fy%2Bhighlight_red%28+%285%2F2%29+%29=4-2%2F%283y%29.
Remove unneeded parentheses around terms highlight_red%28+5%2F2+%29
It becomes 2%2Fy%2Bhighlight_green%28+5%2F2+%29=4-2%2F%283y%29.
Look at 2%2Fy%2B5%2F2=4-highlight_red%28+2%2F%28highlight_red%28+3%2Ay+%29%29+%29.
Remove unneeded parentheses around factor highlight_red%28+1%2F3+%29,highlight_red%28+1%2Fy+%29
It becomes 2%2Fy%2B5%2F2=4-2%2Fhighlight_green%28+3+%29%2Fhighlight_green%28+y+%29.
Look at 2%2Fy%2B5%2F2=highlight_red%28+4+%29-2%2F3%2Fy.
Moved 4 to the right of expression
It becomes 2%2Fy%2B5%2F2=-2%2F3%2Fy%2Bhighlight_green%28+4+%29.
Look at 2%2Fy%2B5%2F2=highlight_red%28+-2%2F3%2Fy%2B4+%29.
Moved these terms to the left highlight_green%28+2%2F3%2Fy+%29,highlight_green%28+-4+%29
It becomes 2%2Fy%2B5%2F2%2Bhighlight_green%28+2%2F3%2Fy+%29-highlight_green%28+4+%29=0.
Look at 2%2Fy%2Bhighlight_red%28+5%2F2+%29%2B2%2F3%2Fy-highlight_red%28+4+%29=0.
Added fractions or integers together
It becomes 2%2Fy-highlight_green%28+3%2F2+%29%2B2%2F3%2Fy=0.
Look at 2%2Fy-highlight_red%28+3%2F2+%29%2B2%2F3%2Fy=0.
Moved -3%2F2 to the right of expression
It becomes 2%2Fy%2B2%2F3%2Fy-highlight_green%28+3%2F2+%29=0.
Look at highlight_red%28+2%2Fy+%29%2Bhighlight_red%28+2%2F3%2Fy+%29-3%2F2=0.
Eliminated similar terms highlight_red%28+2%2Fy+%29,highlight_red%28+2%2F3%2Fy+%29 replacing them with highlight_green%28+%282%2B2%2A1%2F3%29%2Fy+%29
It becomes highlight_green%28+%282%2B2%2A1%2F3%29%2Fy+%29-3%2F2=0.
Look at %282%2Bhighlight_red%28+2+%29%2Ahighlight_red%28+1+%29%2F3%29%2Fy-3%2F2=0.
Multiplied numerator integers
It becomes %282%2Bhighlight_green%28+2+%29%2F3%29%2Fy-3%2F2=0.
Look at %28highlight_red%28+2+%29%2Bhighlight_red%28+2%2F3+%29%29%2Fy-3%2F2=0.
Added fractions or integers together
It becomes %28highlight_green%28+8%2F3+%29%29%2Fy-3%2F2=0.
Look at highlight_red%28+%28highlight_red%28+8%2F3+%29%29%2Fy+%29-3%2F2=0.
Remove unneeded parentheses around factor highlight_red%28+8+%29,highlight_red%28+1%2F3+%29
It becomes highlight_green%28+8+%29%2Fhighlight_green%28+3+%29%2Fy-3%2F2=0.
Result: 8%2F3%2Fy-3%2F2=0

Universal Simplifier and Solver


Done!

from the above
we got +%288%2F3y%29-+3%2F2++=0
move 3/2 to the right
+8%2F3y++=++3%2F2
multiply with 3y on both sides
++%288%2F3y+%29+%2A3y+=++%283%2F2%29%2A3y

divide with 9 on both sides
+16%2F9+=+9y%2F9
16/9 = y

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

solve each equation.
2/y+ 5/2 = 4 - 2/3y


2%2Fy+%2B+5%2F2+=+4+-+2%2F%283y%29 

12 + 15y = 24y - 4 ------- Multiplying by LCD, 6y 

15y - 24y = - 4 - 12

- 9y = - 16

y+=+%28-+16%29%2F%28-+9%29, or highlight_green%2816%2F9%29