Solve For S 78Fa1D

1. **State the problem:** Solve the equation $$-2s + 1 = 3s + 16$$ for the variable $s$. 2. **Write down the formula and rules:** To solve for $s$, we want to isolate $s$ on one side of the equation. We can do this by adding or subtracting terms on both sides and then dividing if necessary. 3. **Step 1: Move all $s$ terms to one side.** Add $2s$ to both sides: $$-2s + 1 + 2s = 3s + 16 + 2s$$ which simplifies to: $$1 = 5s + 16$$ 4. **Step 2: Move constants to the other side.** Subtract $16$ from both sides: $$1 - 16 = 5s + 16 - 16$$ which simplifies to: $$-15 = 5s$$ 5. **Step 3: Solve for $s$ by dividing both sides by $5$:** $$\frac{-15}{\cancel{5}} = \frac{5s}{\cancel{5}}$$ which simplifies to: $$-3 = s$$ or equivalently: $$s = -3$$ 6. **Conclusion:** The solution to the equation is $$s = -3$$. 7. **Check the solution:** Substitute $s = -3$ back into the original equation: Left side: $$-2(-3) + 1 = 6 + 1 = 7$$ Right side: $$3(-3) + 16 = -9 + 16 = 7$$ Both sides equal $7$, so the solution is correct.