Question

8. Graph the solutions for the inequality: −3x+1≤−47
(2 points)
Responses

Answer 1

To solve the inequality \(-3x + 1 \leq -47\), follow these steps:

1. **Isolate the term with \(x\)**:
\[
-3x + 1 \leq -47
\]
Subtract 1 from both sides:
\[
-3x \leq -48
\]

2. **Solve for \(x\)**:
Divide both sides by -3. Remember that when you divide or multiply by a negative number, you must reverse the inequality sign:
\[
x \geq 16
\]

3. **Graph the solution**:
On a number line:

- Draw a number line.
- Place a solid circle at 16 (indicating that 16 is included in the solution).
- Shade the line to the right of 16 to indicate that all numbers greater than or equal to 16 are included in the solution.

Here's a description of how you would represent this graphically:

- **Number line**:

```
------|------|------|------|------|------|------|------|------|------
14 15 16 17 18 19 20 21 22
●======================>
```

In this graph, the solid dot at 16 indicates that 16 is part of the solution, and the arrow indicates that all values greater than 16 are also included.