Question

Solve, graph, and give interval notation for the inequality:
-3-4x>5
0
1
2
3
4
5
-1
-2
-3
-4
-5
Interval notation for the above graph is

Answer 1

To solve the inequality \(-3 - 4x > 5\), we will first isolate \(x\).

1. Add 3 to both sides:
\[
-4x > 5 + 3
\]
\[
-4x > 8
\]

2. Divide both sides by -4. Remember, when you divide by a negative number, you must reverse the inequality sign:
\[
x < \frac{8}{-4}
\]
\[
x < -2
\]

Now we have the solution to the inequality: \(x < -2\).

### Graphing the Solution

To graph this solution:

- Draw a number line.
- Place an open circle at -2 (since -2 is not included in the solution).
- Shade to the left of -2, indicating that all values less than -2 are part of the solution.

### Interval Notation

The interval notation for the inequality \(x < -2\) is:

\[
(-\infty, -2)
\]

### Summary

- Solution: \(x < -2\)
- Interval notation: \((- \infty, -2)\)