Solve the absoulte value inequailty below, expressing your answer in interval notation.

Question

anonymous · Answer

$$\frac{ 1 }{ \left| x+5 \right| }\ge1$$

anonymous · Answer

I've gotten as far as $$-4\ge x$$

anonymous · Answer

and $$-6\le x$$

anonymous · Answer

the problem is that I can't figure out how to write my answer in interval notation

anonymous · Answer

$$-6 \le x \le -4$$

anonymous · Answer

I've gotten it that far, but interval notation is (?,?) or [?,?] or something similar.

anonymous · Answer

oh right sorry

anonymous · Answer

square brackets if it's less than/ greater than and equal to. round brackets if it's not equal to.

anonymous · Answer

< and > are round brackets, $$\le and \ge $$

anonymous · Answer

* are square brackets

anonymous · Answer

So what should the answer be?

anonymous · Answer

[-6,-4] is what I've come up with, but my online program says that is incorrect.

anonymous · Answer

Well that is in interval notation. are you sure -6, -4 is correct?

anonymous · Answer

Yes

rational · Answer

Notice that the expression becomes undefined when $x=-5$, so you need to exclude it from solution

rational · Answer

the solution after excluding would be $$\large [-6,-5) \cup (-5, -4]$$

anonymous · Answer

Thank you! I had tried a similar answer earlier but I must have used the wrong type of brackets.