1. **State the problem:** Solve the linear equation $100x + 95 = 120$ for $x$. 2. **Formula and rules:** To solve for $x$, isolate $x$ on one side of the equation by performing inverse operations. 3. **Step-by-step solution:** - Subtract 95 from both sides: $$100x + 95 - 95 = 120 - 95$$ $$100x = 25$$ - Divide both sides by 100 to solve for $x$: $$x = \frac{25}{100}$$ - Simplify the fraction: $$x = \frac{1}{4}$$ 4. **Answer:** The solution to the equation is $x = \frac{1}{4}$. This means that when $x$ is one quarter, the original equation holds true.