Question

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

2(2x−1)>6 or x+3≤−6

Answer 1

The solution to the compound inequality 2(2x-1)>6 or x+3≤-6 is represented in interval notation as (-∞, -9] ∪ (2, ∞).

Step-by-step explanation:

To solve the compound inequality 2(2x-1)>6 or x+3≤-6, we will address each part of the inequality separately and then determine the combined solution set.

First, let's solve the inequality 2(2x-1)>6:

1. Divide both sides of the inequality by 2: 2x-1 > 3.
2. Add 1 to both sides: 2x > 4.
3. Divide both sides by 2: x > 2.

The solution to this part of the compound inequality in interval notation is (2, ∞).

Now, let's solve the inequality x+3≤-6:

1. Subtract 3 from both sides of the inequality: x ≤ -9.

The solution to this part of the compound inequality is (-∞, -9] in interval notation.

Since the compound inequality uses the word 'or', we combine the solutions. The resulting solution set in interval notation is the union of the two individual solutions:

(-∞, -9] ∪ (2, ∞)