Question

The values of x satisfying $|x-4|+|x-9|=5$, is :

• A. x = 4, 9
• B. 4 $\le$ x $\le$ 9
• C. x $\le$ 4 or x $\ge$ 9
• D. none of these

Answer 1

Answer: (B)

Consider the given equation $|x-4|+|x-9|=5$
$\Rightarrow \{\begin{array}{ll}4-x+9-x=5& x\le 4\\ x-4+9-x=5& 4<x\le 9\\ x-4+x-9=5& x>9\end{array}$
$\Rightarrow \{\begin{array}{ll}x=4& x\le 4\\ 5=5& 4<x\le 9\\ x=9& x>9\end{array}$
So, $4\le x\le 9$