What is the interval notation for this absolute value inequality?

Question

absolute value inequality - l5r + 2l < 18

What is the answer to this in interval notation??

Answer 1

-|5r + 2| &lt; 18

|5r + 2| &gt; -18

Since the term on the left is within an absolute value, it will always be greater than or equal to zero, so it will certainly be greater than a negative number.  This holds for any value of r, so the interval notation is (-∞, ∞).  

Hope this helps you!

Answer 2

-|5r+2| &lt; 18

|5r+2| &gt; -18

5r+2 &gt; 18 and 5r+2 &lt; -18

5r &gt; 16    and  5r &lt; -20

r &gt; 16/5   and  r &lt; -4

so....

(-∞,-4) , (-4,16/5) , (16/5,∞)