The specifications for machining a piece of metal state that it must be 12cm long within a 0.01 cm tolerance. What is the longest the piece is allowed to be ? What is the shortest? Using l to represent the length of the finished piece of metal, write an absolute value inequality that states these conditions.
I have recently studied about absolute value and inequality through some textbooks so I am still kind of shaky. Could you please explain step by step.
Using this notation can be very useful in a problem like the one you've been given, because it can be used to describe the difference between two numbers without having to worry which of the numbers is the bigger, and which is the smaller. So, for instance, the difference between numbers represented by and can be written , and you don't need to worry if is bigger than (which would make negative) because the signs will turn it into a positive number anyway. E.g. the difference between and is .
So, in your problem, we know that the difference between , the actual length, and has to be less than or equal to . So we can simply write
and it doesn't matter whether is bigger than or smaller.