Question

Simplify the following:

$\frac{1}{2}(2x-1)\le 2x+\frac{1}{2}\le 5\frac{1}{2}+x$

• A. $-1\le x\le 5$
  
• B. $1\le x\le 5$
  
• C. $5\le x\le 8$
  
• D. None of these

Answer 1

The correct option is A $-1\le x\le 5$

Since, $\frac{1}{2}(2x-1)\le 2x+\frac{1}{2}\le 5\frac{1}{2}+x$

We have following two cases:

$i)\frac{(2x-1)}{2}\le 2x+\frac{1}{2}$

$\Rightarrow 2x-1\le 4x+1\Rightarrow x\ge -1$

$ii)2x+\frac{1}{2}\le \sqrt{\frac{1}{2}}+x$

$\Rightarrow x\le \frac{11}{2}-\frac{1}{2}\Rightarrow x\le 5$

$\therefore -1\le x\le 5$