Question

How do you solve `15y - \frac { 11} { 2} = \frac { 11} { 2} y + 2`?

Answer 1

You can save yourself some trouble and a possible source of error by multiplying everything by `2`

Explanation:

`->30y-11=11y+4`

Now move the `y`'s to one side, and the numbers to the other, by subtracting `11y` from both sides and adding `11`:

`->30y-cancel11-11y+cancel11=cancel(11y)+4-cancel(11y)+11`

`->19y=15->y=15/19`

Answer 2

`y=15/19`

Explanation:

`"to eliminate the fractions multiply ALL terms by 2 the"`
`"denominator of the fractions"`

`(2xx15y)-(cancel(2)^1xx11/cancel(2)^1)=(cancel(2)^1xx(11y)/cancel(2)^1)+(2xx2)`

`rArr30y-11=11y+4larrcolor(red)" no fractions"`

`"subtract 11y from both sides"`

`30y-11y-11=cancel(11y)cancel(-11y)+4`

`rArr19y-11=4`

`"add 11 to both sides"`

`19ycancel(-11)cancel(+11)=4+11`

`rArr19y=15`

`"divide both sides by 19"`

`(cancel(19) y)/cancel(19)=15/19`

`rArry=15/19`

`color(blue)"As a check"`

Substitute this value into the equation and if left side equals right side then it is the solution.

`"left "=(15xx15/19)-11/2=225/19-11/2=241/38`

`"right "=(11/2xx15/19)+2=165/38+2=241/38`

`rArry=15/19" is the solution"`