Question

The number of integral solution of the inequality $-6<\frac{2x-5}{3}\le 5$ and $-8\le x-7<5$ is

Answer 1

The inequality
$-6<\frac{2x-5}{3}\le 5$
$\Rightarrow -18<2x-5\le 15$
$\Rightarrow -13<2x\le 20$
$\Rightarrow \frac{-13}{2}<x\le 10...\left(1\right)$

and
$-8\le x-7<5$
$-8\le x-7<5$
$\Rightarrow -1\le x<12...\left(2\right)$
From $\left(1\right)$ and $\left(2\right)$
$\Rightarrow -1\le x\le 10$
So, integral values are $\{-1,0,1,...,9,10\}$