Question

Solve the inequality. Graph the solution on the number line and then give the answer in interval notation.
-4-3x≥2
0
1
2
3
4
5
-1
-2
-3
-4
-5
Interval notation for the above graph and inequality is

Answer 1

To solve the inequality \(-4 - 3x \geq 2\), we'll follow these steps:

1. **Isolate the term with \(x\)**:
\[
-3x \geq 2 + 4
\]
Simplifying the right side, we get:
\[
-3x \geq 6
\]

2. **Divide by -3**: Remember that when we divide or multiply both sides of an inequality by a negative number, we must reverse the inequality sign:
\[
x \leq -2
\]

Now we have the solution \(x \leq -2\).

### Graphing the Solution on a Number Line

To graph this solution on a number line:
- Draw a number line with sufficient range to include \(-2\).
- Since the solution includes \(-2\) (indicated by \(\leq\)), we shade to the left of \(-2\) and place a closed circle on the \(-2\) to indicate that it is included in the solution.

### Interval Notation

In interval notation, the solution can be expressed as:
\[
(-\infty, -2]
\]

### Final Answer

Thus, the solution in interval notation is:
\[
(-\infty, -2]
\]