Solve the compound inequality.

Question

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.