Question

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

• A.
• B.
• C.
• D. None of these

Answer 1

The correct option is B

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

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

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