Question

Solve the compound inequality.

5x – 11 < –11 or 4x + 2 > 14


x < –5 or x > 8


x < 0 or x > 4


x < 0 or x > 3


x < or x > 4

Answer 1

Let's solve the given compound inequality step by step.

1. First, solve the left part of the inequality:
\[
5x - 11 < -11
\]
Add 11 to both sides:
\[
5x < 0
\]
Now, divide by 5:
\[
x < 0
\]

2. Next, solve the right part of the inequality:
\[
4x + 2 > 14
\]
Subtract 2 from both sides:
\[
4x > 12
\]
Now, divide by 4:
\[
x > 3
\]

Now we have the solutions for the two parts of the compound inequality:
- From \(5x - 11 < -11\), we found \(x < 0\).
- From \(4x + 2 > 14\), we found \(x > 3\).

Putting these results together, we form the solution to the compound inequality:
\[
x < 0 \quad \text{or} \quad x > 3
\]

Thus, the correct answer is:
- **x < 0 or x > 3**.