Express the fact that #x # differs from 2 by less than#1/ 2# as an inequality involving an absolute value. What is #x#?
1 Answer
Explanation:
What the statement is saying is that the magnitude of the difference between
The difference between
The magnitude of any value or expression can be found by using absolute value.
So the magnitude of the difference can be expressed as
Now, this whole expression is less than
Let's solve this inequality using the properties of absolute value:
If we combine these two results, we get the set
Therefore,