G2.3 If $\ell$ is the minimum value of $|x-2|+|x-47|$, find the value of $\ell$.
Using the triangle inequality: $|a|+|b| \geq|a+b|$
$$
|x-2|+|x-47|=|x-2|+|47-x| \geq|x-2+47-x|=45 \Rightarrow \ell=45
$$