Question

The value(s) of $x$ for which the expression $y=|x+2|+|x-7|$ is minimum is/are

• A. $-4$
• B. $-1$
• C. $5$
• D. $9$

Answer 1

Answer: (B), (C)

The correct options are
B $-1$
C $5$

$y=|x+2|+|x-7|$
Here, the turning points are $-2,7$
$y=\{\begin{array}{cc}-(x+2)-(x-7),& x<-2\\ (x+2)-(x-7),& -2\le x<7\\ (x+2)+(x-7),& x\ge 7\end{array}\Rightarrow y=\{\begin{array}{cc}5-2x,& x<-2\\ 9,& -2\le x<7\\ 2x-5,& x\ge 7\end{array}$

Graph will be

$y$ will be minimum for any value of $x\in [-2,7]$