1. **State the problem:** Solve the inequality $120 + 25x + 10x \geq 300$. 2. **Combine like terms:** $25x + 10x = 35x$, so the inequality becomes: $$120 + 35x \geq 300$$ 3. **Isolate the variable term:** Subtract 120 from both sides: $$120 + 35x - 120 \geq 300 - 120$$ $$35x \geq 180$$ 4. **Divide both sides by 35 to solve for $x$:** $$\frac{\cancel{35}x}{\cancel{35}} \geq \frac{180}{35}$$ $$x \geq \frac{180}{35}$$ 5. **Simplify the fraction:** $$x \geq \frac{36}{7}$$ **Final answer:** $$x \geq \frac{36}{7}$$ This means $x$ must be greater than or equal to $\frac{36}{7}$ for the inequality to hold true.