Question

Solve the compound inequality.

5x – 11 < –11 or 4x + 2 > 14


x < or x > 4


x < –5 or x > 8


x < 0 or x > 3


x < 0 or x > 4

Answer 1

To solve the compound inequality \(5x - 11 < -11\) or \(4x + 2 > 14\), we will solve each inequality separately.

### Solving the first inequality:

1. \(5x - 11 < -11\)

Add 11 to both sides:
\[
5x < -11 + 11
\]
\[
5x < 0
\]

Now, divide by 5:
\[
x < 0
\]

### Solving the second inequality:

2. \(4x + 2 > 14\)

Subtract 2 from both sides:
\[
4x > 14 - 2
\]
\[
4x > 12
\]

Now, divide by 4:
\[
x > 3
\]

### Combining the results:
The solution to the compound inequality is:
\[
x < 0 \quad \text{or} \quad x > 3
\]

So the solution in interval notation is:
\[
(-\infty, 0) \cup (3, \infty)
\]

From the options provided in your question, the answer is:
**x < 0 or x > 3.**