Question

Which of the following expressions does not mean the same as the other three? : x - 17 OR x + (-17) OR x - (-17) OR - 17 + x

Answer 1

x- (-17), the other 3 means you're subtracting 17 from x
While in x- (-17), the 2 subtraction signs cancel out and give you x + 17

Answer 2

Here are the four candidates:
x - 17
x + (-17)
x - (-17)
- 17 + x

When you add a negative number, you're subtracting it.
In other words, when you have + and - next to each other, you end up with subtraction:
x + -17 is the same as x - 17

When you have two terms like "x" and "-17" being added together, you can flip the order around. 2+3 is the same as 3+2 after all, right? (To get technical, this is the commutative property of addition.)
So -17 + x is just x + -17 flipped around.
And we know that x + -17 is the same as x - 17


So here's where we are:
x - 17 = x - 17 (of course :) )
x + (-17) = x - 17
x - (-17)
- 17 + x = x - 17

By process of elimination, we know the answer x - (-17) is the odd man out.


But why?
When you subtract a negative number, you are taking away a negative.
Negatives make a number smaller. If I TAKE AWAY the thing that makes them smaller, then they must get bigger.
In other words, when you subtract a negative, you end up ADDING instead.
Two wrongs don't make a right, but two negatives make a positive. Go figure.

So x - -17 is the same as x + 17
and that's different from the other three.