1. **State the problem:** Solve the linear equation $3x - 1.5 = 16.5$ for $x$. 2. **Formula and rules:** To solve for $x$, isolate $x$ on one side by performing inverse operations. Remember to do the same operation on both sides of the equation. 3. **Add 1.5 to both sides:** $$3x - 1.5 + 1.5 = 16.5 + 1.5$$ $$3x = 18$$ 4. **Divide both sides by 3 to isolate $x$:** $$\frac{\cancel{3}x}{\cancel{3}} = \frac{18}{3}$$ $$x = 6$$ 5. **Final answer:** $x = 6$. This means the value of $x$ that satisfies the equation is 6.