Question

Explain why |x-5|<0 has no solution

Answer 1

The equation is given as,

$\lvert x-5\rvert<0$

Consider that the left-hand side expression is an absolute value function.

The absolute value function always gives a positive value of the output for any given input (x).

This is based on the definition of the absolute value function.

Since the absolute value function always provides a positive value, it can never be negative. So there will be no such value as 'x' for which the absolute value function will give a negative output.

That is why the given equation will have no solution at all.