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

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Solution

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

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