1. **State the problem:** Solve for $\alpha$ in the equation $$25 = 6\alpha + 7$$. 2. **Isolate the term with $\alpha$:** Subtract 7 from both sides: $$25 - 7 = 6\alpha + 7 - 7$$ which simplifies to $$18 = 6\alpha$$ 3. **Divide both sides by 6 to solve for $\alpha$:** $$\frac{18}{\cancel{6}} = \frac{6\alpha}{\cancel{6}}$$ which simplifies to $$3 = \alpha$$ 4. **Final answer:** $$\alpha = 3$$ This means the value of $\alpha$ that satisfies the equation is 3.