1. **State the problem:** Solve the equation $8 \div 2(4 - x) = 1$ for $x$. 2. **Recall the order of operations:** Division and multiplication have the same precedence and are evaluated from left to right. 3. **Rewrite the equation:** $$8 \div 2(4 - x) = 1$$ This means: $$\frac{8}{2} \times (4 - x) = 1$$ 4. **Simplify the division:** $$\frac{8}{2} = 4$$ So the equation becomes: $$4 \times (4 - x) = 1$$ 5. **Distribute 4:** $$4 \times 4 - 4 \times x = 1$$ $$16 - 4x = 1$$ 6. **Isolate the variable term:** $$16 - 4x = 1$$ Subtract 16 from both sides: $$16 - 4x - 16 = 1 - 16$$ $$-4x = -15$$ 7. **Solve for $x$:** Divide both sides by $-4$: $$x = \frac{-15}{\cancel{-4}} \times \cancel{-1} = \frac{15}{4}$$ **Final answer:** $$x = \frac{15}{4}$$