Question

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

Answer 1

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

1. **Isolate the term with \(x\)**: Start by subtracting 1 from both sides of the inequality:
\[
-3x + 1 - 1 \leq -47 - 1
\]
This simplifies to:
\[
-3x \leq -48
\]

2. **Divide by -3**: When you divide or multiply an inequality by a negative number, you must reverse the inequality sign:
\[
x \geq \frac{-48}{-3}
\]
This simplifies to:
\[
x \geq 16
\]

Now that we have the solution \(x \geq 16\), we can graph it on a number line.

### Graphing the solution:

- Draw a number line.
- Place an open circle (or dot) at the point 16 to represent that the solution includes 16 and all numbers greater than 16.
- Shade the region to the right of 16 to indicate all numbers greater than or equal to 16 are part of the solution.

Here is how it would look visually:

```
<---|----|----|----|----|----|----|----|----|----|----|----|----|--->
0 1 2 3 4 5 6 7 8 9 10 11 12 ... 16
●================>
(Shade to the right)
```

In this representation, the point 16 is marked with a solid circle (if closed) to show that 16 is included in the solution. If using a closed dot, the inequality would reflect that \(x\) can equal 16.