SOLUTION: I'm having a hard time with this problem: {{{2/y}}}+{{{5/2}}}=4-{{{2/3y}}} my book is giving the answer 6/19 and I think I keep missing an important step. thank you! -trac

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: I'm having a hard time with this problem: {{{2/y}}}+{{{5/2}}}=4-{{{2/3y}}} my book is giving the answer 6/19 and I think I keep missing an important step. thank you! -trac      Log On


   

Question 12111: I'm having a hard time with this problem:
2%2Fy+5%2F2=4-2%2F3y
my book is giving the answer 6/19 and I think I keep missing an important step. thank you!
-tracy
Answer by bonster(299) About Me  (Show Source):
You can put this solution on YOUR website!
The answer in your book is wrong. If you were to plug in 6%2F19 for the variable y, you would end up with an inequality. The outcome would be 9=21%2F2, which is false.


Here is the solution:
2%2Fy+5%2F2=4-2%2F3y

2%2Fy+21%2F2=4-2%2F3y (((((subtract 21%2F2from both sides

(2%2Fy+21%2F2)-21%2F2=(4-2%2F3y)-21%2F2

2%2Fy=(4-2%2F3y)-21%2F2

2%2Fy=11%2F2-2%2F3y (((add 2%2F3y to both sides

2%2Fy+2%2F3y=11%2F2-2%2F3y+2%2F3y

2%2Fy+2%2F3y=11%2F2

multiply 2%2Fyby 3%2F3

(2%2Fy)(3%2F3)+2%2F3y=11%2F2

6%2F3y+2%2F3y=11%2F2

8%2F3y=1 1%2F2 or 3%2F2

8%2F3y=3%2F2 ((((((multiply both sides by 3y%2F8

(8%2F3y)(3y%2F8)=(3%2F2)(3y%2F8)

1=9y/16 ((((((((multiply both sides by 16%2F9

16%2F91=9y/16 16%2F9

16%2F9=y





....if you were to check your work, plugging in 16%2F9 for the variable y, you'd get 35%2F8=35%2F8which is correct.