Question

The correct statement among the following is

• A. Distance between two points $a,b$ along the number line is given by $|a|-|b|$
• B. $|a|=|b|\Rightarrow a=b$
• C. $|x-5|=5-x\Rightarrow x<5$
• D. Distance between two points $a,b$ along the number line is given by $||a|-|b||$

Answer 1

The correct option is C $|x-5|=5-x\Rightarrow x<5$

Distance between two points $a,b$ along the number line is given by $|a-b|.$

If $|a|=|b|$, then the absolute value of $a,b$ will be same, it is not necessary that their numerical value will also be same.
For eg. $|-2|=|2|$ but $-2\ne 2$

When $x>5$
$|x-5|=x-5$
When $x<5$
$|x-5|=-(x-5)=5-x$