1. **State the problem:** Solve the equation $$\frac{3}{8}m + \frac{7}{8} = 2m$$ for $m$. 2. **Identify the goal:** We want to isolate $m$ on one side of the equation. 3. **Subtract $\frac{3}{8}m$ from both sides:** $$\frac{3}{8}m + \frac{7}{8} - \frac{3}{8}m = 2m - \frac{3}{8}m$$ which simplifies to $$\frac{7}{8} = 2m - \frac{3}{8}m$$ 4. **Combine like terms on the right side:** $$2m - \frac{3}{8}m = \frac{16}{8}m - \frac{3}{8}m = \frac{13}{8}m$$ So the equation is now $$\frac{7}{8} = \frac{13}{8}m$$ 5. **Divide both sides by $\frac{13}{8}$ to solve for $m$:** $$m = \frac{\frac{7}{8}}{\frac{13}{8}}$$ Show the division as multiplication by reciprocal: $$m = \frac{7}{8} \times \frac{8}{13}$$ 6. **Simplify by canceling common factors:** $$m = \frac{7}{\cancel{8}} \times \frac{\cancel{8}}{13} = \frac{7}{13}$$ **Final answer:** $$m = \frac{7}{13}$$