Question

Solve the inequality. Graph the solution on the number line and then give the answer in interval notation.
-4x-4≥8
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 \( -4x - 4 \geq 8 \), we start by isolating \( x \).

1. Add 4 to both sides:
\[
-4x \geq 8 + 4
\]
\[
-4x \geq 12
\]

2. Divide both sides by -4. Remember that when dividing an inequality by a negative number, we must flip the inequality sign:
\[
x \leq \frac{12}{-4}
\]
\[
x \leq -3
\]

The solution to the inequality is \( x \leq -3 \).

### Graphing on the Number Line:
To represent this on a number line:

- Draw a solid dot at -3 (since -3 is included in the solution).
- Shade everything to the left of -3 to indicate that all numbers smaller than -3 are also included in the solution.

### Interval Notation:
The solution in interval notation is:

\[
(-\infty, -3]
\]

This means all real numbers from negative infinity up to and including -3 are solutions to the inequality.