Question

Solve the inequality and graph the solution.
7a+9<2

Answer 1

To solve the inequality \(7a + 9 < 2\), we can follow these steps:

1. **Subtract 9 from both sides:**
\[
7a + 9 - 9 < 2 - 9
\]
This simplifies to:
\[
7a < -7
\]

2. **Divide both sides by 7:**
\[
a < \frac{-7}{7}
\]
This simplifies to:
\[
a < -1
\]

Now we have the solution \(a < -1\).

### Graphing the Solution

To graph the solution on a number line:

- Draw a number line.
- Locate -1 on the number line.
- Use an open circle at -1 to indicate that -1 is not included in the solution (because the inequality is strict).
- Shade the line to the left of -1 to indicate all numbers less than -1.

Here's a textual representation:

```
<----(----|----)---->
-2 -1 0
```

Where:
- The open circle at -1 indicates it's not included in the solution.
- The shaded area to the left of -1 indicates all values less than -1 are part of the solution.