If $| 4 x - 3 | + | x - 4 | = 2$ , then the number of solutions is

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Solution

$| 4 x - 3 | + | x - 4 | = 2$
If $x < \frac{3}{4}$ ,
$- 4 x + 3 - x + 4 = 2$
$\Rightarrow x = 1$ Not possible

If $\frac{3}{4} \leq x < 4$ ,
$4 x - 3 - x + 4 = 2$
$\Rightarrow x = \frac{1}{3}$ Not possible

If $x \geq 4$ ,
$4 x - 3 + x - 4 = 2$
$\Rightarrow x = \frac{9}{5}$ Not possible
Hence, there does not exist any solution.

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