1. **State the problem:** Solve the linear equation $$17 = 5x + 2$$ for $x$. 2. **Isolate the variable term:** Subtract 2 from both sides to get the term with $x$ alone on one side. $$17 - 2 = 5x + 2 - 2$$ $$15 = 5x$$ 3. **Solve for $x$:** Divide both sides by 5 to isolate $x$. $$\frac{15}{\cancel{5}} = \frac{5x}{\cancel{5}}$$ $$3 = x$$ 4. **Final answer:** The solution to the equation is $$x = 3$$.