How do you solve the inequality #2<=abs(4-x)<7# and write your answer in interval notation?
First, recall the rules of absolute values in inequality expressions.
Absolute value is less than something rule
Absolute value is greater than something rule
The inequality we are given can be broken into two parts.
First part: Less than rule
Applying the "less than rule" gives
Second part: Greater than rule
Applying the "greater than rule" gives
Solving both for
Finally, combine all solutions into one
The solution: Either
Here is what the graph would look like: