What is the area of the region defined by the inequality $|3x-18|+|2y+7|\le3$? $\mathrm{(A)}\ 3\qquad$ $\mathrm{(B)}\ \frac {7}{2}\qquad$ $\mathrm{(C)}\ 4\qquad$ $\mathrm{(D)}\ \frac{9}{2}\qquad$ $\mathrm{(E)}\ 5$
Solution
The inequality is $3|x-6|+2|y+\frac72|\le3$, a rhombus centered at $(6,-\frac72)$ whose vertices are $1$ unit from the center horizontally and $\frac32$ units vertically. Its diagonals are $2$ and $3$, so its area is $\frac12\cdot2\cdot3=3$.
