1. **State the problem:** Solve the equation $4x - 13x = -38$ for $x$. 2. **Combine like terms:** On the left side, combine $4x$ and $-13x$. $$4x - 13x = (4 - 13)x = -9x$$ 3. **Rewrite the equation:** $$-9x = -38$$ 4. **Isolate $x$ by dividing both sides by $-9$:** $$x = \frac{-38}{-9}$$ 5. **Simplify the fraction:** $$x = \frac{\cancel{-38}}{\cancel{-9}} = \frac{38}{9}$$ 6. **Final answer:** $$x = \frac{38}{9}$$ This means $x$ is equal to $\frac{38}{9}$, which is approximately $4.22$ when expressed as a decimal.