Question

The values of $x$ which satisfy the inequalities simultaneously
(i) $-3 < 2x - 1 < 19$
(ii) $-1 \le \frac{2x +3}{5} \le 3 $

• A. $[-4, 10)$
• B. $(-1, 6]$
• C. $[-1, 6)$
• D. $(-1, 6)$

Answer 1

Answer: (B)

$-3 < 2x - 1 < 19$
$\Rightarrow -2 < 2x < 20$
$\Rightarrow -1 < x < 10 \,.....(1)$
$-1 \le \frac{2x + 3}{5} \le 3$
$\Rightarrow -5 \le 2x + 3 \le 15$
$\Rightarrow -8 \le 2x \le 12$
$\Rightarrow -4 \le x \le 6\,.....(2)$
Now from $(1)$ and $(2)$ common values are $(-1, 6]$.