4. Construct on the plane the set of points whose coordinates satisfy the inequality $|3 x+4|+|4 y-3| \leq 12$. In your answer, specify the area of the resulting figure.

ANSWER: 24.
Solution: We will shift the coordinate axes by $-\frac{4}{3}$ along the Ox axis, and by $\frac{3}{4}$ along the Oy axis. In the new coordinates, the obtained figure is described by the inequality $|3 x|+|4 y| \leq 12$. It is not difficult to show that this will be a rhombus with diagonals of 6 and 8, therefore, its area is 24.