To solve the inequalities and represent them on a number line, we'll need to work with each inequality separately.
1. 3x - 2y < 10
2. x < 2 + 5x
Let's solve each inequality step by step:
**Inequality 1:**
3x - 2y < 10
First, isolate "y":
-2y < 10 - 3x
Divide both sides by -2 (remember to reverse the inequality when dividing by a negative number):
y > -5 + (3/2)x
**Inequality 2:**
x < 2 + 5x
Subtract "x" from both sides:
0 < 2 + 4x
Subtract "2" from both sides:
-2 < 4x
Divide both sides by 4:
-0.5 < x
Now let's represent these inequalities on a number line:
```
-5 -0.5 2
|-----------|------------|-------->
```
The open circle at -0.5 indicates that x is strictly less than -0.5. The shaded region to the right of the open circle represents values of y greater than -5 + (3/2)x, satisfying the first inequality.