1. **State the problem:** Solve the linear equation $$16 - 2t = 5t + 9$$ for the variable $t$. 2. **Write down the formula and rules:** To solve for $t$, we need to isolate $t$ on one side of the equation by performing inverse operations and maintaining equality. 3. **Step 1: Move all terms involving $t$ to one side and constants to the other:** $$16 - 2t = 5t + 9$$ Subtract $5t$ from both sides: $$16 - 2t - 5t = 5t + 9 - 5t$$ Simplify: $$16 - 7t = 9$$ 4. **Step 2: Move constants to the other side:** Subtract $16$ from both sides: $$16 - 7t - 16 = 9 - 16$$ Simplify: $$-7t = -7$$ 5. **Step 3: Solve for $t$ by dividing both sides by $-7$:** $$t = \frac{-7}{-7}$$ Show cancellation: $$t = \frac{\cancel{-7}}{\cancel{-7}} = 1$$ 6. **Final answer:** $$t = 1$$ This means the value of $t$ that satisfies the equation is 1.