Question

The number of negative integral solution(s) of the inequality $-x<\frac{3x-5}{4}$ and $-5\le x-4<1$ is

Answer 1

The inequality
$-x<\frac{3x-5}{4}$
$\Rightarrow -4x<3x-5$
$\Rightarrow -7x<-5$
$\Rightarrow x>\frac{5}{7}...\left(1\right)$
and
$-5\le x-4<1$
$\Rightarrow -1\le x<5...\left(2\right)$
From $\left(1\right)$ and $\left(2\right)$
$\Rightarrow \frac{5}{7}<x<5$
There is no negative integral value.