1. **Stating the problem:** We have the inequality $$7000x_1 + 10000x_2 + 5000x_3 \leq 200000$$ and we want to understand or solve it for the variables $x_1$, $x_2$, and $x_3$. 2. **Understanding the inequality:** This is a linear inequality representing a constraint on the variables $x_1$, $x_2$, and $x_3$. The coefficients 7000, 10000, and 5000 represent weights or costs associated with each variable. 3. **Formula and rules:** The inequality can be interpreted as a linear combination of variables bounded above by 200000. To find feasible solutions, values of $x_1$, $x_2$, and $x_3$ must satisfy: $$7000x_1 + 10000x_2 + 5000x_3 \leq 200000$$ 4. **Example of solving for one variable:** If we want to express $x_1$ in terms of $x_2$ and $x_3$, rearrange: $$7000x_1 \leq 200000 - 10000x_2 - 5000x_3$$ Divide both sides by 7000 (assuming $7000 > 0$): $$x_1 \leq \frac{200000 - 10000x_2 - 5000x_3}{7000}$$ 5. **Interpretation:** This inequality defines a region in 3D space where the weighted sum of $x_1$, $x_2$, and $x_3$ does not exceed 200000. 6. **Summary:** The inequality is a linear constraint useful in optimization or feasibility problems. Solutions must satisfy the above condition.