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Q.
Set of values of x satisfying the inequality $ \frac{x^2 + 6x - 7}{ |x + 4|} < 0$ is / are
Linear Inequalities
Solution:
$\frac{ x ^2+6 x -7}{| x +4|}<0 \Rightarrow x ^2+6 x -7<0$ provided
$x +4 \neq 0[\because| x +4|>0$ if $x \neq-4]$
$\Rightarrow( x +7)( x -1)<0, x \neq-4$
$\Rightarrow-7< x <1, x \neq-4$
$\therefore x \in(-7,-4) \cup(-4,1)$