If x satisfies the inequalities x + 7

Question

If x satisfies the inequalities x + 7 < 2x + 3 and 2x + 4 < 5x + 3 , then x lies in the interval (A) (-∞,3) (B) (1,3) (C) (4,∞) (D) ( - ∞ ,- l)

Tardigrade Admin · Accepted Answer

Given, x+7< 2 x+3 ⇒ 4 ≤ x ⇒ x> 4 dots(i) and 2 x+4< 5 x+3 ⇒ 1< 3 ⇒ x > (1/3) dots(ii) From Eqs. (i) and (ii), we get the common interval (4, ∞) i.e., x ∈(4, ∞)

Q. If $x$ satisfies the inequalities $x + 7 < 2 x + 3$ and $2 x + 4 < 5 x + 3$ , then $x$ lies in the interval

(- $\infty$ ,3)

(1,3)

(4, $\infty$ )

( - $\infty$ ,- l)

(3,4)

Given,
$x + 7 < 2 x + 3$
$\Rightarrow 4 \leq x$
$\Rightarrow x > 4 \dots (i)$
and $2 x + 4 < 5 x + 3$
$\Rightarrow 1 < 3$
$\Rightarrow x > \frac{1}{3} \dots (ii)$
From Eqs. (i) and (ii), we get the common interval $(4, \infty)$ i.e., $x \in (4, \infty)$

Q. If x satisfies the inequalities x+7<2x+3 and 2x+4<5x+3 , then x lies in the interval

(-∞,3)