I want to solve the following optimization problem in $x\in\mathbb{R}$
$$\begin{array}{ll} \text{minimize} & |ax+b|+|cx+d|\\ \text{subject to} & x \in [x_1,x_2] \cup [x_3,x_4]\end{array}$$
where $[x_1,x_2] \cap [x_3,x_4]=\emptyset$. Is there a way to transform it to a LP form?