1. Stating the problem: Solve the equation $$\frac{1}{7}x = -8$$ for $x$. 2. Formula and rules: To solve for $x$ when it is multiplied by a fraction, multiply both sides of the equation by the reciprocal of that fraction. 3. Intermediate work: Multiply both sides by 7: $$7 \times \frac{1}{7}x = 7 \times (-8)$$ Simplifies to: $$x = -56$$ 4. Explanation: Multiplying both sides by 7 cancels the denominator 7 on the left side, leaving $x$ alone. On the right side, $7 \times -8$ equals $-56$. 5. Final answer: $$x = -56$$