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. **Isolate the variable**: 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**: Remember that when you divide or multiply both sides of an inequality by a negative number, you need to flip the inequality sign:
\[
x \geq \frac{-48}{-3}
\]
Simplifying that gives:
\[
x \geq 16
\]

Now, we can graph the solution \(x \geq 16\):

- On a number line, draw a solid dot at 16 (indicating that 16 is included in the solution since the inequality is "greater than or equal to").
- Shade to the right of 16 to indicate all numbers greater than 16 are included in the solution set.

Your final graph representation should look like this:

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

This indicates that all values \(x\) that are 16 and greater are included in the solutions.