Question

Question #a7e8c

Answer 1

`y=31/5`

Explanation:

`1/(y-6)=5`
To solve for y, we first begin by multiplying `y-6` to both sides to get the `y-6` out of denominator of the left-hand side:
`(y-6)*1/(y-6)=5(y-6)`
Now we can use the distributive property on the 5 on the right-hand side to expand:
`1=5y-30`
Next we add 30 to both sides to put the constants on one side:
`31=5y`
Finally we divide both sides by 5 to isolate the y variable:
`y=31/5`
Therefore, our final answer is `y=31/5`.

Answer 2

See a solution process below:

Explanation:

Multiply each side of the equation by `(color(red)(y - 6))/color(blue)(5)` to eliminate the fraction while keeping the equation balanced:

`(color(red)(y - 6))/color(blue)(5) xx 1/((y - 6)) = (color(red)(y - 6))/color(blue)(5) xx 5`

`cancel((color(red)(y - 6)))/color(blue)(5) xx 1/color(red)(cancel(color(black)((y - 6)))) = (color(red)(y - 6))/cancel(color(blue)(5)) xx color(blue)(cancel(color(black)(5)))`

`1/5 = y - 6`

Now, add `color(red)(6)` to each side of the equation to solve for `y` while keeping the equation balanced:

`1/5 + color(red)(6) = y - 6 + color(red)(6)`

`1/5 + (5/5 xx color(red)(6)) = y - 0`

`1/5 + 30/5 = y`

`(1 + 30)/5 = y`

`31/5 = y`

`y = 31/5`