https://file.aiquickdraw.com/mathbot/file/1726889893736pbbs42jm.jpg

The image contains a set of linear inequalities. Let's write them out in a more formal way:

1. \( 5x_1 + 2x_2 \geq 10 \)
2. \( 2x_1 + 5x_2 \geq 10 \)
3. \( 4x_1 - x_2 \geq 12 \)
4. \( x_1 + x_2 \geq 4 \)
5. \( x_1, x_2 \geq 0 \)

These inequalities define a feasible region in the \(x_1x_2\)-plane for linear programming or optimization problems.

Would you like a detailed explanation of how to solve this system or visualize the feasible region? Here are some questions you might be interested in:

1. What is the graphical representation of these inequalities?
2. How to find the optimal solution for a linear programming problem with these constraints?
3. How do these inequalities intersect, and what is the feasible region?
4. How to check if a given point is feasible for this system?
5. Can we add an objective function to optimize within these constraints?

**Tip:** To solve linear inequalities, it's often helpful to graph them and identify the region of overlap, which represents the solution set.

Solve the system of linear inequalities:
1. 5x₁ + 2x₂ ≥ 10
2. 2x₁ + 5x₂ ≥ 10
3. 4x₁ - x₂ ≥ 12
4. x₁ + x₂ ≥ 4
5. x₁, x₂ ≥ 0

Explore how to solve a system of linear inequalities, including 5x₁ + 2x₂ ≥ 10 and other inequalities. Understand key concepts in linear programming and how to graphically find the feasible region.

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