Question

Step 1: Solve and graph this inequality:



`-3x-1\ge11`

Answer 1

To solve the inequality \(-3x - 1 \ge 11\), follow these steps:

1. **Isolate the variable**: Start by adding \(1\) to both sides:

\[
-3x - 1 + 1 \ge 11 + 1
\]
\[
-3x \ge 12
\]

2. **Divide by -3**: Remember that dividing or multiplying both sides of an inequality by a negative number flips the inequality sign:

\[
x \le \frac{12}{-3}
\]
\[
x \le -4
\]

Now we have the solution to the inequality: \(x \le -4\).

Next, we will graph this inequality on a number line.

### Graphing the inequality:

1. **Draw a number line**.
2. **Locate -4 on the number line**. Since the inequality is \(x \le -4\), we will use a solid dot at \(-4\) to indicate that \(-4\) is included in the solution.
3. **Shade to the left of \(-4\)**: This represents all the numbers less than or equal to \(-4\).

The graph represents all values of \(x\) that satisfy the inequality \(x \le -4\):

```
<---|---|---|---|---|---|---|--->
-5 -4 -3 -2 -1 0 1
●<==================

```

Here, `●` at \(-4\) indicates that \(-4\) is included in the solution. The shading on the left shows all values less than \(-4\).