Question

Find the number of values of x which satisfy the relation $|x-4|$ +$|x-8|$ = 4

• A. 1
• B. 2
• C. No solution
• D. Infinite number of x

Answer 1

The correct option is D

Infinite number of x

Let f(x) = $|x-4|$ + $|x-8|$

We have to find f(x) in the intervals ($-\infty$, 4), [4,8] and [8,$\infty$].

Let's consider the interval [4,8] first.(you can follow your own order)

4 $\le$ x $\le$ 8

$|x-4|=x-4and|x-8|$= 8 - x

$\Rightarrow$ f(x) = x - 4 + 8 - x

= 4

So all the number (rational and irrational) between 4 and 8 satisfy the relation, so the number of solution is infinite.