1. **State the problem:** Solve the linear equation $$-9 = \frac{2}{7}x + 5$$ for $x$. 2. **Isolate the term with $x$:** Subtract 5 from both sides to get $$-9 - 5 = \frac{2}{7}x + 5 - 5$$ which simplifies to $$-14 = \frac{2}{7}x$$ 3. **Solve for $x$:** Multiply both sides by the reciprocal of $\frac{2}{7}$, which is $\frac{7}{2}$: $$x = -14 \times \frac{7}{2}$$ 4. **Simplify the multiplication:** $$x = \cancel{-14} \times \frac{7}{2} = -7 \times 7 = -49$$ 5. **Final answer:** $$x = -49$$