3x + y < 10

To graph the inequality 3x + y < 10, we can start by graphing the equation 3x + y = 10, which is the boundary line.

To graph the equation 3x + y = 10, we can rearrange it to solve for y:
y = -3x + 10

Now we can plot the points on the graph:
When x = 0, y = 10
When x = 1, y = 7
When x = 2, y = 4

Plotting these points and drawing a line through them, we get:

```
|
10| /
| /
| /
| /
|/
+-----------------
0 1 2 3 4 5
```

Now, since the inequality is less than (<), we need to determine which side of the line to shade. We can choose a test point, such as (0, 0), and substitute it into the inequality:

3(0) + 0 < 10
0 < 10

Since the inequality is true, we shade the side of the line that contains the point (0, 0).

Shading the appropriate side of the line, we get:

```
|
10| /
| / shade here
| /
| /
|/
+-----------------
0 1 2 3 4 5
```

Therefore, the solution to the inequality 3x + y < 10 is the shaded region below the line.