1. **State the problem:** Solve the linear equation $4m + 5 = 35 - 2m$ for $m$. 2. **Write down the equation:** $$4m + 5 = 35 - 2m$$ 3. **Add $2m$ to both sides** to get all $m$ terms on one side: $$4m + 2m + 5 = 35 - \cancel{2m} + 2m$$ $$6m + 5 = 35$$ 4. **Subtract 5 from both sides** to isolate the term with $m$: $$6m + 5 - 5 = 35 - 5$$ $$6m = 30$$ 5. **Divide both sides by 6** to solve for $m$: $$\frac{6m}{\cancel{6}} = \frac{30}{\cancel{6}}$$ $$m = 5$$ 6. **Final answer:** $$m = 5$$ This means the value of $m$ that satisfies the equation is 5.