Question

Graph the solutions for the inequality: −3x+1≤−47

Answer 1

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

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

2. **Solve for \(x\)**:
Divide both sides by \(-3\). Remember, dividing by a negative number flips the inequality sign:
\[
x \geq \frac{-48}{-3}
\]
Simplifying this gives:
\[
x \geq 16
\]

Now we can interpret the inequality \(x \geq 16\). This means that \(x\) takes on values 16 and greater.

### Graphing the Solution

1. **Draw a number line.**
2. **Place a closed circle at 16** to indicate that 16 is included in the solution (since the inequality is "greater than or equal to").
3. **Shade the area to the right of 16** to indicate all numbers greater than 16 are part of the solution.

Here’s a representation of the graph:

```
<----|----|----|----|----|----|----|----|----|---->
13 14 15 16 17 18 19 20 21 22
●=========================>
```

In this representation:
- The circle at 16 is closed (●) because 16 is included in the solution.
- The arrow indicates that the solution includes all numbers greater than 16.