Question

$\text{If x}ϵZ,\text{solve the inequation}2+4x<2x-5\le 3x.\text{Also, represent its solution set on a number line.}$

• A.
• B.
• C.
• D. None of these

Answer 1

The correct option is B

$\text{It is given that}2+4x<2x-5\le 3x$
$\Rightarrow 2+4x<2x-5\text{and}2x-5\le 3x$
$\Rightarrow 4x-2x<-5-2\text{and}-5\le x$
$\Rightarrow 2x<-7\text{and}-5\le x$
$\Rightarrow x<\left(\frac{-7}{2}\right)\text{and x}\le -5$
$\Rightarrow -5\le \text{x and x}<-\left(\frac{7}{2}\right)$
$\Rightarrow -5\le x<-\left(\frac{7}{2}\right)$
But, $\text{x}ϵZ.$
$\therefore -5\le x<-\left(\frac{7}{2}\right)\text{and x}ϵZ\Rightarrow x=-5,-4$

Hence, the solution set is [-5, -4 ]

The graphical representation of the solution set on a number line is as follows: