Question

solve and graph 5m+12 less than 12 or 7m greater than 49

Answer 1

To solve the inequalities \(5m + 12 < 12\) and \(7m > 49\), we'll address each inequality separately.

### Solving the first inequality:
1. Start with the inequality:
\[
5m + 12 < 12
\]
2. Subtract 12 from both sides:
\[
5m < 0
\]
3. Divide by 5:
\[
m < 0
\]

### Solving the second inequality:
1. Start with the inequality:
\[
7m > 49
\]
2. Divide by 7:
\[
m > 7
\]

### Combining the solutions:
The solution set for the first inequality is \(m < 0\) and for the second inequality is \(m > 7\). Since this is a compound inequality with "or," the solution set combines both parts:

- The final solution is:
\[
m < 0 \quad \text{or} \quad m > 7
\]

### Graphing the solution:
- On a number line, we will represent \(m < 0\) with an open circle on 0 and shading to the left.
- For \(m > 7\), we will represent it with an open circle on 7 and shading to the right.

Here is a rough representation of the graph:

```
<---O=================O--->
-1 0 7
```

- The open circles indicate that 0 and 7 are not included in the solution set. The shaded areas show that all values less than 0 and greater than 7 are included in the solution.