Question

Solve the inequality and graph the solution.
3m–7>5

Answer 1

To solve the inequality \(3m - 7 > 5\), we'll start by isolating \(m\).

1. Add 7 to both sides:
\[
3m - 7 + 7 > 5 + 7
\]
Simplifying gives:
\[
3m > 12
\]

2. Next, divide both sides by 3:
\[
m > \frac{12}{3}
\]
Simplifying gives:
\[
m > 4
\]

So, the solution to the inequality is:
\[
m > 4
\]

### Graphing the Solution

To graph the solution \(m > 4\):

- Draw a number line.
- Place a point above 4, indicating that 4 is not included (since it is a strict inequality).
- Shade to the right of 4 to indicate that all numbers greater than 4 are included in the solution.

This indicates that \(m\) can take any value greater than 4.

Here is a simple ASCII representation of the graph:

```
<---|---|---|---|---|---|---|---|---|---|--->
... 3 4 5 6 7 8 9 ...
(-------->
```

In this representation, the parenthesis at 4 shows that it is not included in the solution and the arrow indicates that the solution continues to infinity to the right.