How can I remember to set up an equation like this problem?

Whenever you’re solving a question like that, you always want to end up with only one (possibly more) number on the opposite side of the letter.

Once you write y – 15 + 15 = -7 + 15, that simplifies to y = 8 (once you do the math). You want to get the y alone (or whichever variable you are trying to solve for).

single variable equations are all about getting the variable by itself, and the way to do that is to move the terms through the equation sign to the other side, but this can only be accomplished by doing the opposite of what was being done on the original side.

for example, y/2 -31 = 1

think of the – 31 as a +(-31) if it helps you

start by taking the added or subtracted terms to the other side

dragging the 31 through the = changes the sign

y/2 = 31 + 1 = 32

there is still the /2 attached to the y, so you have to multiply when you drag it through the =

y = 32 * 2 = 64

The way I learned it a dog’s age ago is to think of the equation as being like a scale; What you do to one side of the = sign, you have to do the other side. When you are trying to get the variable (the letter for the unknown term on one side), you need to do what you have to do to make zero on the side of the equation that the variable is on. If you have a negative number, you have to add the same number. Because you need to balance, you need to do it on both sides of the equation. A positive number plus the negative of that number always equals zero.

In your example, y – 15 = -7, to get y by itself you have to add 15 to each side, because
-15 +15 = 0, and this puts y by itself (y-0 = y)
Because you need to keep the equation balanced, you need to also add 15 to the other side,
or -7 + 15, which equals 8, or y = 8.

Honestly, I think you are letting it intimidate you a bit.

You did exactly the right thing in the sample equation you listed, and after putting a +15 on both sides to get y – 15 + 15 = -7 + 15, there really isn’t any “after that” except simply combining the terms with simple addition.

y – 15 + 15 = y , since the +15 and -15 cancel each other out
-7 + 15 = 8 , and that is probably the hardest part

You are better at this than you think :)