1. **State the problem:** Solve the linear equation $109x + 98 = 120$ for $x$. 2. **Formula and rules:** To solve for $x$, isolate $x$ by performing inverse operations. Subtract 98 from both sides, then divide both sides by 109. 3. **Step-by-step solution:** - Subtract 98 from both sides: $$109x + 98 - 98 = 120 - 98$$ $$109x = 22$$ - Divide both sides by 109: $$x = \frac{22}{109}$$ 4. **Final answer:** $$x = \frac{22}{109}$$ This fraction cannot be simplified further, so this is the exact solution. 5. **Explanation:** We used basic algebraic operations to isolate the variable $x$. Subtracting 98 removes the constant term on the left, and dividing by 109 undoes the multiplication by 109, leaving $x$ alone.