Solve the equation for y...?

First subtract that 7 from the left side

7/y = -15

Now take the inverse of both equations. So basically do 1 divided by everything. This flips the fraction on the left and makes -15 turn into 1/-15

y/7 = 1/-15

multiply both sides by 7 and that's that

y = -7/15

No need to set it to anything.
1st interpretation:
7/(y + 7) = - 8
- 8(y + 7) = 7
- 8y - 56 = 7
8y = - 63
y = - 63/8

Answer: y = - 63/8

Check:
7/(- 63/8 + 7) = - 8
7/(- 63/8 + 56/8) = - 8
7/(- 7/8) = - 8
7(- 8/7) = - 8
- 8 = - 8

2nd interpretation:
(7/y) + 7 = - 8
7/y = - 15
- 15y = 7
y = - 7/15

Answer: y = - 7/15

Check:
(7/[- 7/15]) + 7 = - 8
(7[- 15/7]) + 7 = - 8
- 15 + 7 = - 8
- 8 = - 8

No. It will be solved as
7/y + 7 = -8
7/y = -15
7 = -15y
7/-15 = y

So,
y = -7/15

7/y + 7 = -8
7/y = -8 - 7
7/y = -15
7 = -15y
y = -15/7
y = -1 1/7

7/-15

What you want to do when you're solving for y is to separate every number to one side and have the variable (y) alone on the other side.

(7/y) +7= -8

First, subtract 7 to move it over to the right side of the equation.

(7/y) +7 = -8
Which gives you (7/y)= -15
To get the 7 out of the numerator (because y needs to be by itself, you just do the opposite operation. If you take a look at the original equation, I moved the 7 over by doing the opposite operation. It originally added 4, so I did the opposite and subtracted.
(7/y) is 7 divided by y, so, the opposite of division is multiplication.

Multiply both sides by (1/7). I picked the (1/7) because (7/1) times (1/7) is (7/7), which is 1.
So, you'll have:

1 over y on the left side and -15/7 on the right.
Since y is still not by itself, you aren't done yet.
Any number or letter over 1 is that number or letter. 5 over 1 is 5. 6 over 1 is 6. x over 1 is x, etc...
So, flip the fraction to make 1/y equal to y. Remember, if you do something to one side of the equal sign, you NEED to do it to the other side of the equal sign. So, we need to flip -15/7 which gives us 7/-15


We are finished because the y is isolated.
y= 7/-15

Check your work by plugging in y= (7/-15) to the origination equation.

(7) / (7/-15) + 7= -8

Firstly, bring over the 7 on the left hand side to the right hand side such that the equation looks like this:
7/y=-7-8
7/y=-15
Then, we cross multiply the equation
7/y x -15/1
Therefore, we get
-15y=7
So, we can conclude that y=-7/15.

lets do it the easy way
7/y+7=-8
7/y = -8-7
7/y= -15
7/y X y = -15 X y
7 = -15y
7/-15 = y

here is your answer y = -7/15
or
y = .4666666666666666666...

assume (7/y) + 7 = -8
NO, Move the 7 to the right side

7/y = -8 -7 =-15
Now swap y and -15
7/-15 = y or y = -7/15

What troubles me is do you mean :-
Question (i)
(7/y) + 7 = - 8
OR
Question (ii)
7 / (y + 7) = - 8 ?

Let us do both :-

Question (i)
(7/y) = - 15
7 = - 15 y
y = - 7 / 15

Question (ii)
7 = - 8 (y + 7)
7 = - 8y - 56
8y = - 63
y = - 63/8