Answer
$F_{fr} \leq \mu_s ~F_N$
Work Step by Step
$F_{fr} \leq \mu_s ~F_N$
We need to use the < sign because the force of static friction does not necessarily exert its maximum possible force in all situations. The force of static friction can vary from zero to its maximum possible force of $\mu_s ~F_N$. We would use the equals sign in the equation only when the force of static friction is at its maximum possible force; $\mu_s ~F_N$.
For example, if a cup is just sitting at rest on a table, the force of static friction is zero. If we exert a small force, say 1 N, on the cup, then the force of static friction will push back with an equal and opposite force of 1 N. We can continue increasing the applied force gradually, and the cup will not start moving until we apply enough force to overcome the maximum possible force of static friction, which is $\mu_s ~F_N$.
