Question

Graph the inequality and give interval notation for the solution. Use two o's (as in octopus) for infinity and a U for union as needed.
-5x-2>13 OR -9x-1≤-37
0
1
2
3
4
5
-1
-2
-3
-4
-5
interval notation for the above inequality and graph is

Answer 1

To solve the compound inequality \(-5x - 2 > 13\) OR \(-9x - 1 \leq -37\), we'll solve each inequality separately.

### 1. Solve \(-5x - 2 > 13\)

First, isolate \(x\):

\[
-5x > 13 + 2
\]

\[
-5x > 15
\]

Now, divide by \(-5\) and reverse the inequality sign:

\[
x < -3
\]

### 2. Solve \(-9x - 1 \leq -37\)

Again, isolate \(x\):

\[
-9x \leq -37 + 1
\]

\[
-9x \leq -36
\]

Divide by \(-9\) and reverse the inequality sign:

\[
x \geq 4
\]

### 3. Combine the Solutions

We have two inequalities:

1. \(x < -3\)
2. \(x \geq 4\)

Since this is an "OR" statement, the solution includes all \(x\) that satisfy either inequality.

### 4. Interval Notation

The interval notation for these solutions will be:

\[
(-\infty, -3) \cup [4, \infty)
\]

### 5. Graphing the Solution

To graph the solution:

- Draw a number line.
- For \(x < -3\), put an open circle at -3 and shade to the left towards \(-\infty\).
- For \(x \geq 4\), put a closed circle at 4 and shade to the right towards \(+\infty\).

### Final Answer

**Interval notation:** \((-oo, -3) \cup [4, oo)\)

Feel free to ask if you have questions or need further explanation!