Why is it important to follow the order of operations instead of solving from left to right?
a math expression has meaning in it, it is not just a bunch of operations. The older of operations is a set of rule that everybody will follow so that we have a solid foundation to communicate with each other so that the meaning in an expression can be delivered without distortion.
For example:
5-2*3
according to the order of operation, it means the difference between 5 and the product of 2 and 3; without order of operation, it would mean3 times of the difference between 5 and 2. Totally two different meanings.