Question

Solve the inequality and graph the solution on the line provided.
8, x, minus, 7, is greater than or equal to, minus, 39
8x−7≥
−39
Answer


Inequality Notation:
Number Line:

Answer 1

To solve the inequality \( 8x - 7 \geq -39 \), follow these steps:

1. **Add 7 to both sides**:
\[
8x - 7 + 7 \geq -39 + 7
\]
This simplifies to:
\[
8x \geq -32
\]

2. **Divide both sides by 8**:
\[
x \geq -4
\]

### Solution
The final result is:
- **Inequality Notation**: \( x \geq -4 \)

### Graphing on a Number Line
To graph the solution on a number line:
- Draw a number line.
- Mark the point \(-4\).
- Since the inequality is greater than or equal to (\( \geq \)), use a closed dot on \(-4\) to indicate that \(-4\) is included in the solution.
- Shade the line to the right of \(-4\) to represent all numbers greater than \(-4\).

Here's a textual representation of the graph:

```
<---|----|----|----|----|----|----|--->
-5 -4 -3 -2 -1 0 1
●====================>
```

In the above graph:
- The dot on \(-4\) represents that \(-4\) is included.
- The shaded line to the right indicates all values greater than \(-4\).