What is the area of the region defined by the [inequality](https://artofproblemsolving.com/wiki/index.php/Inequality) $|3x-18|+|2y+7|\le3$?
$\mathrm{(A)}\ 3\qquad\mathrm{(B)}\ \frac{7}{2}\qquad\mathrm{(C)}\ 4\qquad\mathrm{(D)}\ \frac{9}{2}\qquad\mathrm{(E)}\ 5$
Area is invariant under translation, so after translating left $6$ and up $7/2$ units, we have the inequality
\[|3x| + |2y|\leq 3\]
which forms a [diamond](https://artofproblemsolving.com/wiki/index.php/Rhombus) centered at the [origin](https://artofproblemsolving.com/wiki/index.php/Origin) and vertices at $(\pm 1, 0), (0, \pm 1.5)$. Thus the diagonals are of length $2$ and $3$. Using the formula $A = \frac 12 d_1 d_2$, the answer is $\frac{1}{2}(2)(3) = 3 \Rightarrow \mathrm{(A)}$.