1. **State the problem:** We need to solve the equation $$\frac{1}{3} - 4 = \frac{T}{5} + 1$$ for the variable $T$. 2. **Simplify the left side:** Convert $4$ into a fraction with denominator 3: $$4 = \frac{12}{3}$$ So, $$\frac{1}{3} - \frac{12}{3} = \frac{1 - 12}{3} = \frac{-11}{3}$$ 3. **Rewrite the equation:** $$\frac{-11}{3} = \frac{T}{5} + 1$$ 4. **Isolate the term with $T$:** Subtract $1$ from both sides: $$\frac{-11}{3} - 1 = \frac{T}{5}$$ Convert $1$ to a fraction with denominator 3: $$1 = \frac{3}{3}$$ So, $$\frac{-11}{3} - \frac{3}{3} = \frac{-14}{3}$$ 5. **Expression for $T/5$:** $$\frac{T}{5} = \frac{-14}{3}$$ 6. **Solve for $T$:** Multiply both sides by 5: $$T = 5 \times \frac{-14}{3} = \frac{-70}{3}$$ **Final answer:** $$T = \frac{-70}{3}$$