1. **State the problem:** Solve the literal equation $$-ax + 6 = -21$$ for the variable $$x$$. 2. **Formula and rules:** To solve for $$x$$, isolate $$x$$ on one side of the equation using inverse operations such as addition, subtraction, multiplication, and division. 3. **Step 1:** Subtract 6 from both sides to isolate the term with $$x$$: $$-ax + 6 - 6 = -21 - 6$$ which simplifies to $$-ax = -27$$ 4. **Step 2:** Divide both sides by $$-a$$ to solve for $$x$$: $$x = \frac{-27}{-a}$$ Show cancellation: $$x = \frac{\cancel{-}27}{\cancel{-}a} = \frac{27}{a}$$ 5. **Final answer:** $$x = \frac{27}{a}$$ This means $$x$$ is equal to 27 divided by $$a$$, assuming $$a \neq 0$$ to avoid division by zero. This process uses basic algebraic principles to isolate the variable of interest in a literal equation.