1. The first equation is $\frac{m - 3}{4} = \frac{m + 1}{3}$. We are given the LCD is 12. 2. Multiply both sides by 12 to clear the denominators: $$12 \times \frac{m - 3}{4} = 12 \times \frac{m + 1}{3}$$ This simplifies to: $$3(m - 3) = 4(m + 1)$$ 3. Expand both sides: $$3m - 9 = 4m + 4$$ 4. Subtract $3m$ from both sides: $$-9 = m + 4$$ 5. Subtract 4 from both sides to isolate $m$: $$-9 - 4 = m$$ $$-13 = m$$ 6. So the solution to the first equation is: $$m = -13$$ 7. The second equation is $\frac{3c - 2}{5} = \frac{2c - 1}{3}$. We are given the LCD is 15. 8. Multiply both sides by 15 to clear denominators: $$15 \times \frac{3c - 2}{5} = 15 \times \frac{2c - 1}{3}$$ This simplifies to: $$3(3c - 2) = 5(2c - 1)$$ 9. Expand both sides: $$9c - 6 = 10c - 5$$ 10. Subtract $9c$ from both sides: $$-6 = c - 5$$ 11. Add 5 to both sides to isolate $c$: $$-6 + 5 = c$$ $$-1 = c$$ 12. So the solution to the second equation is: $$c = -1$$