To model the expression 3(X + 2) + 2x using tiles, we can use rectangular tiles to represent the value of X. Each tile represents one unit of X. We can also use square tiles to represent the constant terms in the expression, which are 3, 2, and 2x.
First, we can model 3(X + 2) by placing three rectangular tiles in a row, and then placing two more rectangular tiles to the right of them. This represents the expression 3(X + 2), or three times the quantity X plus two.
Next, we can add 2x to the expression by placing 2x square tiles to the right of the rectangular tiles. This represents the full expression 3(X + 2) + 2x.
In total, we have modeled the expression using three rectangular tiles (representing 3X), four square tiles (representing 2, 2, 2x, and 2x), and the two grouping symbols (parentheses) that indicate the order of operations.
Here is an example of what the model might look like:
```
XXX XX
■ ■ ■ ■
■ ■ ■ ■
■ ■
```
In this model, the rectangular tiles represent X, the square tiles represent constants, and the grouping symbols are not represented by tiles, but can be seen in the expression 3(X + 2) + 2x.