1. Stating the problem: Solve the equation $$\frac{m - 3}{4} = \frac{m + 1}{3}$$ for $m$. 2. To eliminate the fractions, multiply both sides of the equation by the least common denominator, which is 12 (since 4 and 3 are denominators). 3. Multiply each term: $$12 \times \frac{m - 3}{4} = 12 \times \frac{m + 1}{3}$$ This simplifies to: $$3(m - 3) = 4(m + 1)$$ 4. Expand both sides: $$3m - 9 = 4m + 4$$ 5. Rearrange the equation to isolate $m$ on one side. Subtract $3m$ from both sides: $$-9 = 4m - 3m + 4$$ Which simplifies to: $$-9 = m + 4$$ 6. Subtract 4 from both sides to isolate $m$: $$-9 - 4 = m$$ 7. Simplify the left side: $$-13 = m$$ Final answer: $$m = -13$$