Jerry had some action figures on a shelf in his room. Later he added w more action figures to the shelf. If there are a total of x action figures on his shelf now How many action figures did he have initially on the shelf?
1) Let's call the number of action figures Jerry initially had on the shelf $a$.

2) Let's call the number of action figures Jerry added to the shelf $b$.

3) Then, the number of action figures Jerry has on the shelf now, $x$, is equal to:

$$x = a + b$$

4) We are told in the problem that the total number of action figures on Jerry's shelf is now $x$. So:

$$x = a + b$$

5) We are told in the problem that Jerry had some action figures on a shelf in his room initially. So:

$$a > 0$$

6) We are told in the problem that later Jerry added more action figures to the shelf. So:

$$b > 0$$

7) Solving for $a$, we get:

$$a = x - b$$

Thus, the number of action figures Jerry had initially on the shelf is equal to the total number of action figures on his shelf now, $x$, minus the number of action figures Jerry added to the shelf, $b$.