Question

Find the value of $x$ which satisfies the equation $1-2\left[x\right]=-3$. ( $\left[x\right]$ represents the greatest integer less than or equal to $x$).

• A. $x=2$
• B. $2\le x<3$
• C. $2<x\le 3$
• D. $2<x<3$
• E. There is no solution

Answer 1

The correct option is B $2\le x<3$

Given, $1-\mid 2x\mid =-3$

$\therefore 1-2x\le -3$

$\Rightarrow -2x\le -3-1$

$\Rightarrow -2x\le -4$

$\Rightarrow x\le 2$

Then, $1-2x<-3+-2$

$\Rightarrow -2x<-6$

$\Rightarrow x<3$

$\Rightarrow 2\le x<3$