4. Plot on the plane $(x ; y)$ the set of points satisfying the equation $|15 x|+|8 y|+|120-15 x-8 y|=120$, and find the area of the resulting figure.
Answer: 60.

Solution. Note that the equality $|a|+|b|+|c|=a+b+c$ holds if and only if the numbers $a, b$, and $c$ are non-negative (since if at least one of them is negative, the left side is greater than the right). Therefore, the first equation is equivalent to the system of inequalities

$$
\left\{\begin{array} { l } 
{ 1 5 x \geq 0 , } \\
{ 8 y \geq 0 , } \\
{ 1 2 0 - 1 5 x - 8 y \geq 0 }
\end{array} \Leftrightarrow \left\{\begin{array}{l}
x \geq 0 \\
y \geq 0 \\
15 x+8 y \leq 120
\end{array}\right.\right.
$$

This system defines a triangle on the plane with vertices $E(8 ; 0), G(0 ; 15), N(0 ; 0)$, the area of which is equal to 60.