Opposites

5 and −5 are opposites. Both sit five steps from zero, one on each side.

The minus sign has two jobs

In −5 it says which side of zero. In −(5) it says "the opposite of". They agree here, which is why it is written the same way.

The opposite of an opposite

−(−5) means the opposite of −5, which is 5. Two reversals land you back where you started.

Zero is unusual

Zero is its own opposite. It is nought steps from itself in either direction.

Same distance, other side

The opposite of 5 is −5, and the opposite of −5 is 5. Opposites sit the same distance from zero on either side, so they have the same absolute value and different signs. Zero is its own opposite.

Opposites add to zero

5 + (−5) = 0. Adding a number and its opposite always gives zero, which is why the opposite is also called the additive inverse. This is the property that makes solving equations by adding to both sides work.

The opposite of an opposite

−(−5) = 5. Taking the opposite twice returns you to where you started, because you crossed zero and came back. That is why two minus signs in a row cancel — not by a rule about signs, but because of what "opposite" means.

The minus sign does two jobs

In 7 − 5 the sign means subtract; in −5 it means the opposite of 5. Context decides which. This double duty is genuinely confusing at first, and the way through it is to read each expression carefully rather than looking for a rule.