1. **State the problem:** Solve the equation $5 - 13x = 4 + 9x$ for $x$. 2. **Write the formula and rules:** To solve linear equations, we isolate the variable $x$ by performing the same operations on both sides of the equation. 3. **Step-by-step solution:** - Start with the equation: $$5 - 13x = 4 + 9x$$ - Move all terms involving $x$ to one side and constants to the other: $$5 - 13x - 9x = 4 + 9x - 9x$$ $$5 - 22x = 4$$ - Subtract 5 from both sides: $$5 - 22x - 5 = 4 - 5$$ $$\cancel{5} - 22x - \cancel{5} = -1$$ $$-22x = -1$$ - Divide both sides by $-22$ to solve for $x$: $$x = \frac{-1}{-22}$$ $$x = \frac{1}{22}$$ 4. **Final answer:** $$x = \frac{1}{22}$$ This means the value of $x$ that satisfies the equation is $\frac{1}{22}$.