With these types of problems, it's all about luck. You have to try every combo you can think of before landing on the answer.
Fortunately, there aren't too many combos to try out. There's also a fairly methodical process to make sure you try every combo.
I'll start having the left parenthesis at the very left side. The right parenthesis will steadily march through the expression.
- (30)-4x3+5 = 30-12+5 = 23
- (30-4)x3+5 = 26x3+5 = 78+5 = 83
- (30-4x3)+5 = (30-12)+5 = 23
- (30-4x3+5) = 23
So far, no good. The goal of course is to get a result of 2. Let's now place the left parenthesis immediately after the 30. Like before, the right parenthesis will progress steadily through until we each the right most side.
- 30(-4)x3+5 = 30(-12)+5 = -360+5 = -355
- 30(-4x3)+5 = 30(-12)+5 = -360+5 = -355
- 30(-4x3+5) = 30(-12+5) = 30(-7) = -210
We haven't found it here either.
Let's place the parenthesis just after the minus sign.
- 30-(4)x3+5 = 30-12+5 = 23
- 30-(4x3)+5 = 30-12+5 = 23
- 30-(4x3+5) = 30-(12+5) = 30-17 = 13
Still not what we want.
Let's place the parenthesis just after the multiplication symbol x.
- 30-4x(3)+5 = 30-12+5 = 23
- 30-4x(3+5) = 30-4x8 = 30-32 = -2 ... close but not quite
We land on -2 which I think your teacher might have been going for. Unfortunately (as far as I can see), it's not possible to insert one set of parenthesis and have the expression 30-4x3+5 become 2.
