1. **State the problem:** Solve the equation $$\frac{6x - 2}{2} = x + 9$$ for $x$. 2. **Use the formula and rules:** To solve for $x$, first eliminate the fraction by multiplying both sides by 2. 3. Multiply both sides by 2: $$2 \times \frac{6x - 2}{2} = 2 \times (x + 9)$$ This simplifies to: $$\cancel{2} \times \frac{6x - 2}{\cancel{2}} = 2x + 18$$ which is: $$6x - 2 = 2x + 18$$ 4. **Isolate $x$ terms:** Subtract $2x$ from both sides: $$6x - 2x - 2 = 2x - 2x + 18$$ which simplifies to: $$4x - 2 = 18$$ 5. **Isolate constant terms:** Add 2 to both sides: $$4x - 2 + 2 = 18 + 2$$ which simplifies to: $$4x = 20$$ 6. **Solve for $x$:** Divide both sides by 4: $$\frac{4x}{4} = \frac{20}{4}$$ which simplifies to: $$\cancel{4}x / \cancel{4} = 5$$ so $$x = 5$$ **Final answer:** $$x = 5$$