This is a compound inequality (double inequality) of the form $a \leq \frac{3x+11}{2} \leq b$. Following the method shown in Example 10 from the Miscellaneous Examples, we solve both inequalities simultaneously by applying the same operation to all three parts. First, multiply by 2 to clear the denominator, then subtract 11, and finally divide by 3 to isolate x. The solution includes all real numbers from 1 to 11/3, inclusive.