Question

Graph the solutions for the inequality: -3x + 1<-47

Answer 1

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

1. **Isolate the variable term**:
- Subtract 1 from both sides:
\[
-3x < -47 - 1
\]
\[
-3x < -48
\]

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

The solution to the inequality is \(x > 16\).

### Graphing the Solution:

On a number line:

- Draw a number line and mark the point at 16.
- Since the inequality is \(x > 16\), you will use an open circle at 16 to indicate that 16 is not included in the solution.
- Shade the line to the right of 16 to show that all numbers greater than 16 are part of the solution.

Here's a simple representation:

```
<---|----|----|----|----|----|----|----|----|----|--->
10 11 12 13 14 15 16 (open circle)
>
```

This graph indicates that all values greater than 16 are solutions to the inequality.