The number of integral values of $x, x > - 10$ satisfying the inequality $- 5 (x - 1) + 3 > 3 x - 4$ are:

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Solution

Given: $- 5 (x - 1) + 3 > 3 x - 4$
$\Rightarrow - 5 x + 5 + 3 > 3 x - 4$
$\Rightarrow - 5 x + 8 > 3 x - 4$
$\Rightarrow - 5 x + 8 + 5 x > 3 x - 4 + 5 x [add 5 x on both the sides of the inequality]$

$\Rightarrow 8 > 8 x - 4$

$\Rightarrow 8 + 4 > 8 x - 4 + 4 [add 4 on both the sides of the inequality]$

$\Rightarrow 12 > 8 x$

$\Rightarrow \frac{12}{8} > \frac{8 x}{8} [divide by 8 on both the sides of the inequality]$

$\Rightarrow \frac{3}{2} > x$
$\Rightarrow x \in (- \infty, \frac{3}{2}) \Rightarrow x \in (- \infty, 1.5)$
Since, $x > - 10$
Integral values of $x$ satisfying the conditions are $x = - 9, - 8, - 7, - 6, - 5, - 4, - 3, - 2, - 1, 0, 1.$

$∴$ The number of integral values of $x$ is $11.$

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