Question

The number of integral values satisfying the inequality
$\frac{(x+2)(x-7)}{(x+3{)}^4}<0\text{is}$

Answer 1

Given
$\frac{(x+2)(x-7)}{(x+3{)}^4}<0$
We know that $(x+3{)}^4$ is always positive
So, the inequality becomes,
$(x+2)(x-7)<0,x\ne -3\text{Using wavy curve method}\Rightarrow x\in (-2,7)$

The required integral values are $\{-1,0,1,2,3,4,5,6\}$
Hence, number of integral values are $8$.