1. **State the problem:** Solve the equation $-2a + 7 = a - 8$ for $a$. 2. **Write the equation:** $$-2a + 7 = a - 8$$ 3. **Isolate variable terms on one side:** Add $2a$ to both sides: $$7 = a + 2a - 8$$ Simplify: $$7 = 3a - 8$$ 4. **Isolate the constant term:** Add $8$ to both sides: $$7 + 8 = 3a$$ $$15 = 3a$$ 5. **Solve for $a$:** Divide both sides by $3$: $$a = \frac{15}{3}$$ $$a = 5$$ **Final answer:** $$a = 5$$