To solve this inequality, we need to expand the left side of the equation and simplify it.

(x+1)(x+2)(x+3)(x+4) = x^4 + 10x^3 + 35x^2 + 50x + 24

Now we need to set this expression less than 3:

x^4 + 10x^3 + 35x^2 + 50x + 24 < 3

Rearranging the terms, we get:

x^4 + 10x^3 + 35x^2 + 50x + 21 < 0

Next, we need to find the roots of the equation so that we can determine the intervals where the inequality holds true.

The roots of the equation can be difficult to find, so we can use numerical methods or graphing software to determine the intervals where the inequality is satisfied.

For simplicity, let's examine the values of x that make the inequality true by trying some values in each interval.

By trying x = -5, -1, 0, 1, and 5, we can see that the inequality holds true for -5 < x < -3 and -1 < x < 1.

Therefore, the solution to the inequality (x+1)(x+2)(x+3)(x+4)<3 is -5 < x < -3 and -1 < x < 1.