1. **State the problem:** Solve the equation $6x - 4 - 2x + 5 = 13$ for $x$. 2. **Combine like terms:** Group the $x$ terms and the constants separately. $$6x - 2x - 4 + 5 = 13$$ 3. Simplify the terms: $$4x + 1 = 13$$ 4. **Isolate the variable term:** Subtract 1 from both sides. $$4x + \cancel{1} - \cancel{1} = 13 - 1$$ $$4x = 12$$ 5. **Solve for $x$:** Divide both sides by 4. $$\frac{4x}{\cancel{4}} = \frac{12}{\cancel{4}}$$ $$x = 3$$ **Final answer:** $x = 3$