How do you solve and write the following in interval notation: #1/|x+5| >2#?
1 Answer
Explanation:
First of all, we have to exclude the value when the inequality is undefined because the denominator is zero:
In all cases, except this,
Both sides of an inequality can be multiplied by a POSITIVE number, leaving the sign of inequality as is.
Since
or
Next transformation is division of both sides of inequality by POSITIVE number
Recall the definition of
Consider now two cases (we excluded
Case 1.
Then
or, subtracting
We have to combine this with an inequality that defines our case,
Both inequalities result in'
Case 2.
Then
or, add
or, subtracting
We have to combine this with an inequality that defines our case,
Both inequalities result in'
Final solution is
Here is an illustrative graph of a function
graph{1/|x+5|-2 [-10, 2, -5, 5]}