GATE ECE 2022 | GA Question: 7

Question

Consider the following inequalities.

• A. $2x – 1 > 7$
• B. $2x – 9 < 1$

Which one of the following expressions below satisfies the above two inequalities?

• A. $x \leq – 4$
• B. $ – 4 < x \leq 4$
• C. $4 < x < 5$
• D. $x \geq 5$

Answer 1

Given that, 

• $2x – 1>7 \quad \longrightarrow (1)$
• $2x-9<1 \quad \longrightarrow (2)$

From equation $(1),$

$2x-1>7$

$\Rightarrow 2x >8$

$\Rightarrow  {\color{Blue} {\boxed {x > 4}}}$

From equation $(2),$

$2x – 9<1$

$\Rightarrow 2x<10$

$\Rightarrow  {\color{Red} {\boxed {x < 5}}}$

We can write, ${\color{Green} {\boxed {4<x < 5}}}$

Correct Answer $:\text{C}$