Answer:
1. to add 9 to both sides
2. to multiply by 2 to both sides (horrible English)
3. x = -8
Explanation:
why do you feel you are terrible at this ?
this is like a riddle or puzzle to solve. like a magic cube or changing a match in a pattern of matches to create another pattern.
let's try and explain this to you.
an equation is like a balance, where both cups are in perfect balance.
whatever value is on the left side, is exactly also on the right side. although it is not plainly visible and explainable, why they are equal.
so, to find out we need to transform the equation. and to keep the balance while transforming you have to do the same changes on both sides of the balance. until you find out what makes the cups equal.
if we destroy the balance at any point, we have no more chance to find out what made both sides equal in the first place, because there is no more original balance.
we can do all mathematical operations in the transformation.
we can add things, subtract things, multiply by a factor, divide by something, ... - anything.
x/2 - 9 = -13
to get clarity in our search for the reason of the equality we try to combine the same type of terms on one side of the equation, and the other type (or types) on the other side.
what types of terms do we have here ?
there is one with a variable (x/2), and there are constant terms (-9, -13).
so, what do I need to do to get rid of the constant term (-9) on the side of the variable term (so that this becomes the side with only variable terms) ?
I need to add 9, so the constant term on that side turns 0 and therefore disappears in the sum. but remember, the action has to be done on both sides.
so,
x/2 - 9 = -13 | + 9 on both sides
x/2 - 9 + 9 = -13 + 9
x/2 = -4
what else is now blocking our view on what x is ?
there is this 1/2 factor of x.
how do we get rid of this 1/2 ? by multiplying by 2. because 2× 1/2 = 1, and a factor of 1 disappears in a multiplication.
x/2 = -4 | ×2 on both sides
x/2 × 2 = -4 × 2
x = -8
and now we see what it is that kept both cups or sides in balance : x = -8