1. **State the problem:** Solve the equation $2x + 5 = 17x$ for $x$. 2. **Formula and rules:** To solve linear equations, we isolate the variable on one side by performing inverse operations. 3. **Step 1:** Subtract $2x$ from both sides to get all $x$ terms on one side: $$2x + 5 - 2x = 17x - 2x$$ which simplifies to $$5 = 15x$$ 4. **Step 2:** Divide both sides by 15 to solve for $x$: $$\frac{5}{\cancel{15}} = \frac{15x}{\cancel{15}}$$ which simplifies to $$x = \frac{5}{15}$$ 5. **Step 3:** Simplify the fraction: $$x = \frac{1}{3}$$ **Final answer:** $$x = \frac{1}{3}$$