1. **State the problem:** Solve the equation $6x = 18 + 4x$ for $x$. 2. **Write down the formula and rules:** To solve linear equations, we isolate the variable on one side by performing the same operation on both sides. 3. **Subtract $4x$ from both sides:** $$6x - \cancel{4x} = 18 + \cancel{4x} - 4x$$ which simplifies to $$2x = 18$$ 4. **Divide both sides by 2 to solve for $x$:** $$\frac{2x}{\cancel{2}} = \frac{18}{\cancel{2}}$$ which simplifies to $$x = 9$$ 5. **Final answer:** $$x = 9$$ This means the value of $x$ that satisfies the equation is 9.