It is a fact that -7 is NOT greater than -3. In fact, -7 is less than -3. This can be understood by looking at their position on the number line as explained below.

Consider the positions of -7 and -3 as indicated on the number line.

This is because when we are comparing any two numbers on the real line the number which occurs more towards the right-hand side is considered to be “greater” than the number which occurs on the left. That is why, for instance, we consider 9 to be greater than 6 since 9 occurs to the right of the number line.

Therefore by looking at the number line above we conclude that -7 (on the left) is less than -3 (on the right). Another way to see this is that whenever we are comparing two negative numbers, the number closer to zero is always greater than the number that is farther away from zero. Since -3 is closer to 0 and -7 is farther away from 0 we see that -3 is indeed greater than -7.