Question

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

Answer 1

To graph the solutions for the inequality \(-3x + 1 \leq -47\), we first need to solve the inequality for \(x\).

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

2. **Divide both sides by -3** (remember to reverse the inequality sign when dividing by a negative number):
\[
x \geq \frac{-48}{-3}
\]
\[
x \geq 16
\]

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

### Graphing the solution:

To graph the solution on a number line:

1. Draw a number line.
2. Mark the point \(16\) on the number line.
3. Since the inequality is \(x \geq 16\), you will use a **closed circle** at \(16\) to indicate that \(16\) is included in the solution set.
4. Shade the region to the right of \(16\) to show all numbers greater than \(16\).

This visually represents that all values of \(x\) starting from \(16\) and going to infinity are solutions to the inequality.