Shade the region given by inequality
`2x + y ge 6`

Explanation

To solve the inequality \(2x + y \geq 6\) and shade the appropriate region, follow these steps:

### Step 1: Convert the inequality to an equation
First, we convert the inequality into an equation to find the boundary line:
\[ 2x + y = 6 \]

### Step 2: Find the intercepts
To graph the line, we can find the x-intercept and y-intercept.

- **Finding the x-intercept**: Set \(y = 0\):
\[ 2x + 0 = 6 \implies 2x = 6 \implies x = 3 \]
So the x-intercept is \((3, 0)\).

- **Finding the y-intercept**: Set \(x = 0\):
\[ 2(0) + y = 6 \implies y = 6 \]
So the y-intercept is \((0, 6)\).

### Step 3: Plot the intercepts on the graph
Now, plot the points \((3, 0)\) and \((0, 6)\) on a Cartesian plane.

### Step 4: Draw the boundary line
Since the inequality is \(\geq\), we will draw a solid line through the points \((3, 0)\) and \((0, 6)\) to indicate that points on the line are included in the solution set.

### Step 5: Determine the shading direction
To find out which side of the line to shade, we can test a point not on the line. A common choice is the origin \((0, 0)\).

Substituting \((0, 0)\) into the inequality:
\[ 2(0) + 0 \geq 6 \implies 0 \geq 6 \quad \text{(False)} \]
Since this statement is false, we shade the opposite side of the line from the origin.

### Step 6: Shade the appropriate region
Shade the region above the line \(2x + y = 6\) to represent the solution set of the inequality \(2x + y \geq 6\).

---