Question

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. **Subtract 1 from both sides**:
\[
-3x \leq -47 - 1
\]
\[
-3x \leq -48
\]

2. **Divide both sides by -3**. Remember that when you divide or multiply by a negative number, you must flip the inequality sign:
\[
x \geq \frac{-48}{-3}
\]
\[
x \geq 16
\]

### Graphing the Solution:

1. On a number line, mark the point \(16\).
2. Since the inequality is \(x \geq 16\), you will use a **closed dot** at \(16\) to indicate that \(16\) is included in the solution set.
3. Shade the line to the **right** of the dot to represent all values greater than \(16\).

Here’s a simple representation:

```
<---|---|---|---|---|---|---|---|---|---|--->
15 16 17 18 19
●======================>
```

- The closed dot (●) indicates that \(16\) is included, and the shading to the right indicates that all values greater than \(16\) are part of the solution.