Finding x Values for x + 4 > 2/|x+3|: Algebraic Solution

[phospho]

find the values of x for which

x + 4 > \dfrac{2}{|x+3|}

as the | x + 3 | is positive I thought it would be okay to just bring it over so:

(x+4)(x+3) &gt; 2 solving this, I get x > -2 and x < - 5

however drawing a sketch of the original question shows that the only value needed is x > - 2

my question is why doesn't my method work, and is there a way to do this algebraically without any graph drawing?

 

[eumyang]

as the | x + 3 | is positive I thought it would be okay to just bring it over so:

(x+4)(x+3) &gt; 2 solving this, I get x > -2 and x < - 5

It may be okay to "just bring it over," but that does not mean you can drop the absolute value symbol. You still need them:
(x+4)|x+3| &gt; 2

my question is why doesn't my method work, and is there a way to do this algebraically without any graph drawing?

Make a sign chart. Find values that make the original inequality 0 or undefined, and plot them on a number line:

<--------+--------+--------+-------->
        -5       -3       -2

Test a value in each interval to see if the inequality holds.