Question

What is the solution to the compound inequality in interval notation?

[2(2x – 1) > 6 or x + 3 < -6]
A) (-[infinity], – 9) or (2, 0)
B) (-[infinity], – 9) or (2, [infinity])
C) (-[infinity], – 9) or (2, 0)
D) [-9, 2)

Answer 1

To solve the compound inequality, solve each inequality separately and then combine the solutions. The solution in interval notation is (-∞, -9) or (2, ∞).

Step-by-step explanation:

To solve the compound inequality, we need to solve each inequality separately and then combine the solutions.

For the first inequality, 2(2x - 1) > 6, we can simplify it to get 4x - 2 > 6. Adding 2 to both sides gives us 4x > 8, and dividing both sides by 4 gives us x > 2.

For the second inequality, x + 3 < -6, we can subtract 3 from both sides to get x < -9.

Combining the solutions gives us the intervals (-∞, -9) and (2, ∞). So the solution in interval notation is: (-∞, -9) or (2, ∞).