1. **State the problem:** Solve the linear equation $4m + 3 = 13 - m$ for $m$. 2. **Write down the equation:** $$4m + 3 = 13 - m$$ 3. **Add $m$ to both sides** to get all $m$ terms on one side: $$4m + m + 3 = 13$$ $$5m + 3 = 13$$ 4. **Subtract 3 from both sides** to isolate the term with $m$: $$5m = 13 - 3$$ $$5m = 10$$ 5. **Divide both sides by 5** to solve for $m$: $$m = \frac{10}{5}$$ $$m = 2$$ **Final answer:** $m = 2$