The values of x which satisfy the inequalities simultaneously (i) -3

Question

The values of x which satisfy the inequalities simultaneously (i) -3 < 2x - 1 < 19 (ii) -1 le (2x +3/5) le 3  (A) [-4, 10) (B) (-1, 6] (C) [-1, 6) (D) (-1, 6)

Tardigrade Admin · Accepted Answer

-3 < 2x - 1 < 19 ⇒ -2 < 2x < 20 ⇒ -1 < x < 10 .....(1) -1 le (2x + 3/5) le 3 ⇒ -5 le 2x + 3 le 15 ⇒ -8 le 2x le 12 ⇒ -4 le x le 6 .....(2) Now from (1) and (2) common values are (-1, 6].

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

$[- 4, 10)$

$(- 1, 6]$

$[- 1, 6)$

$(- 1, 6)$

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

Q. The values of x which satisfy the inequalities simultaneously (i) −3<2x−1<19 (ii) −1≤52x+3​≤3

[−4,10)

(−1,6]

[−1,6)

(−1,6)