Brake pad/lining dust can often be the cause of brake squealing when brakes are applied. This is normally remedied by blowing dust out with compressed air.
If your rotors are warped or uneven, this will make a squealing sound. You may need to have your rotors turned or replaced.
I would check two things immediately...brake wear being the first, as most pads are now equipped with "sensors" that contact the spinning rotor to create a reminder squeal. Change the brakes at this point. Second thing would be brake dust as mentioned above, HOWEVER, it is not good practice to blow brake dust with anything. At this point, the rotors must be resurfaced to remove the "glaze" caused by heat and friction to their surfaces. Remember, when resurfacing rotors, or drums, replace all pads and shoes.
Some occasional squealing can be a normal characteristic on many vehicles. Also, if you tend to let the car sit without use for days at a time, learn to live with the squeal. A few drum brake systems (Neon rear drum brakes are of note) have a design that is inherently squeaky.
If you're using low quality brake pads switch to a better grade.
If they believe that your brakes are unsafe, they can stop you and force you to get an inspection. I don't think that they legally have a leg to stand on ticketing you for your brakes being loud. On another note, if your brakes are squealing, odds are that you need new pads and if you wait too long, you will need rotors as well. Change them before it costs you more.
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