Question

Solve the inequality and graph the solution.
2.5m–1.5(2–3m)>2(m+1)
Plot the endpoints. Select an endpoint to change it from closed to open. Select the middle of the segment, ray, or line to delete it.

Answer 1

To solve the inequality \(2.5m - 1.5(2 - 3m) > 2(m + 1)\), we will start by simplifying both sides of the inequality.

1. **Simplify the left side**:

\[
2.5m - 1.5(2 - 3m) = 2.5m - 1.5 \times 2 + 1.5 \times 3m
\]
\[
= 2.5m - 3 + 4.5m
\]
\[
= (2.5m + 4.5m) - 3
\]
\[
= 7m - 3
\]

2. **Simplify the right side**:

\[
2(m + 1) = 2m + 2
\]

3. **Set the inequality**:

Now we combine both sides:

\[
7m - 3 > 2m + 2
\]

4. **Subtract \(2m\) from both sides**:

\[
7m - 2m - 3 > 2
\]
\[
5m - 3 > 2
\]

5. **Add 3 to both sides**:

\[
5m > 5
\]

6. **Divide by 5**:

\[
m > 1
\]

### Graphing the Solution

- The solution \(m > 1\) has an open endpoint at \(m = 1\) because the inequality does not include \(1\).
- Since it is a greater than inequality, we will shade to the right of \(1\).

### Graph

- Draw a number line.
- Plot an open circle at point \(1\) (to indicate that \(1\) is not included).
- Shade the area to the right of \(1\) to indicate all numbers greater than \(1\).

**Final Output**:

The solution to the inequality is:

\[
m > 1
\]

And the graphical representation would look like this:

```
|
1 •--------------
|
```

Where the circle at \(1\) is not filled (open circle) indicating that \(m\) can take any value greater than \(1\).