The absolute value of a number is the positive version of that number. So, if
is positive, its absolute value is
itself. If
is negative, its absolute value is
, so that it will be positive again.
So, if the absolute value of a number is smaller than a certain quantity, i.e. it means that the positive version of
is less than
.
So, if is positive, the inequality becomes
. If
is negative, the inequality becomes
.
So, as a compound inequality, we have
So, in your case, we have
Add 8 to all sides in this inequality:
So, on a number line, you must higlight all numbers between 7.79 and 8.01, endpoints excluded.
Conceptually, this means that the bolt measurement should be exactly 8mm, but you can accept bolts that are 0.01 millimeters shorter of larger.
