Solve `2x + 5y ge 10`

Explanation

To solve the inequality \(2x + 5y \geq 10\), we will follow these steps:

### Step 1: Convert the inequality to an equation
First, we convert the inequality into an equation to find the boundary line:
\[ 2x + 5y = 10 \]

### Step 2: Find the intercepts
Next, we will find the x-intercept and y-intercept of the line.

- **Finding the y-intercept**: Set \(x = 0\):
\[ 2(0) + 5y = 10 \implies 5y = 10 \implies y = 2 \]
So, the y-intercept is \((0, 2)\).

- **Finding the x-intercept**: Set \(y = 0\):
\[ 2x + 5(0) = 10 \implies 2x = 10 \implies x = 5 \]
So, the x-intercept is \((5, 0)\).

### Step 3: Plot the points
Now, we will plot the points \((0, 2)\) and \((5, 0)\) on a graph.

### Step 4: Draw the boundary line
Next, we draw a straight line through the points \((0, 2)\) and \((5, 0)\). Since the inequality is \(\geq\), we will draw a solid line to indicate that points on the line are included in the solution.

### Step 5: Determine the feasible region
To find the feasible region, we can test a point not on the line. A common choice is the origin \((0, 0)\):
\[ 2(0) + 5(0) = 0 \quad \text{which is not } \geq 10 \]
Since this point does not satisfy the inequality, the feasible region will be the area above the line.

### Step 6: Shade the feasible region
Finally, we shade the region above the line, which represents all the points \((x, y)\) that satisfy the inequality \(2x + 5y \geq 10\).

### Summary of the solution
The solution to the inequality \(2x + 5y \geq 10\) is the shaded region above the line \(2x + 5y = 10\), including the line itself.

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