Question

Given
A = {$x:11x-5>7x+3,xϵR$}
B = {$x:18x-9\ge 15+12x,xϵR$}
The range of set $A\cap B$ is .

• A. $\{x\ge 4\}$
• B. $\{x\le 4\}$
• C. $\{x=4\}$
• D. $\{x>4\}$

Answer 1

The correct option is A $\{x\ge 4\}$

Given: $A=\{x:11x-5>7x+3,xϵR\}$
$11x-5>7x+3$

Rule: If a term of an inequation is transferred from one side to the other side of the inequation, the sign of the term gets changed. Let's apply this rule in the above inequation.

$\Rightarrow 4x>8$
$\Rightarrow x>2$

Given: $B=\{x:18x-9\ge 15+12x,xϵR\}$
$\Rightarrow 18x-9\ge 15+12x$

Rule: If a term of an inequation is transferred from one side to the other side of the inequation, the sign of the term gets changed. Let's apply this rule in the above inequation.

$\Rightarrow 6x\ge 24$
$\Rightarrow x\ge 4$
So $A\cap B=x\ge 4$