1. **State the problem:** Solve the equation $5 - 4x + 3 = -30$ for $x$. 2. **Combine like terms on the left side:** $$5 + 3 - 4x = -30$$ $$8 - 4x = -30$$ 3. **Isolate the term with $x$ by subtracting 8 from both sides:** $$8 - 4x - 8 = -30 - 8$$ $$\cancel{8} - 4x - \cancel{8} = -38$$ $$-4x = -38$$ 4. **Solve for $x$ by dividing both sides by $-4$:** $$\frac{-4x}{-4} = \frac{-38}{-4}$$ $$x = \frac{38}{4}$$ 5. **Simplify the fraction:** $$x = \frac{19}{2}$$ **Final answer:** $$x = \frac{19}{2}$$