1. **State the problem:** Solve the linear equation $-5x + 4 = -4x + 9$ for $x$. 2. **Write down the equation:** $$-5x + 4 = -4x + 9$$ 3. **Isolate the variable terms on one side:** Add $5x$ to both sides: $$\cancel{-5x} + 4 + 5x = -4x + 9 + 5x$$ which simplifies to $$4 = x + 9$$ 4. **Isolate $x$ by subtracting 9 from both sides:** $$4 - 9 = x + \cancel{9} - 9$$ which simplifies to $$-5 = x$$ 5. **Final answer:** $$x = -5$$ This means the value of $x$ that satisfies the equation is $-5$.