Question

Given:

$A=\{x:11x-5>7x+3,x\in R\}$ and

$B=\{x:18x-9\ge 15+12x,x\in R\}$.

Find the range of set $A\cap B$.

• A. $\{x:x\in Randx>2\}$
• B. $\{x:x\in Randx>4\}$
• C. $\{x:x\in Randx\ge 2\}$
• D. $\{x:x\in Randx\ge 4\}$

Answer 1

The correct option is D

$\{x:x\in Randx\ge 4\}$

Consider first inequation A,

$11x-5>7x+3$

$\Rightarrow 4x>8$

$\Rightarrow x>2$

Consider second inequation B,

$18x-9\ge 15+12x$

$\Rightarrow 6x\ge 24$

$\Rightarrow x\ge 4$

$A\cap B$ includes range common to both A and B.

So, range of $A\cap B$ is given by $\{x:x\in Randx\ge 4\}$