Question

Solve each compound inequality. Write your answer in interval notation or if no solutions exist write no solutions.

(a) x<0 or x ≥ 14:
(b) x ≤ 10 or x ≥ 4:

Answer 1

(-∞, 10] ∪ [4, ∞)

Explanation:

Let's solve each compound inequality:

(a) x < 0 or x ≥ 14:

For the first part of the compound inequality, x < 0, the solution set is all real numbers less than 0, represented as (-∞, 0).

For the second part, x ≥ 14, the solution set is all real numbers greater than or equal to 14, represented as [14, ∞).

To find the solution to the compound inequality, we combine these two solution sets using the union (or) symbol:

(-∞, 0) ∪ [14, ∞)

So, in interval notation, the solution is (-∞, 0) ∪ [14, ∞).

(b) x ≤ 10 or x ≥ 4:

For the first part of the compound inequality, x ≤ 10, the solution set is all real numbers less than or equal to 10, represented as (-∞, 10].

For the second part, x ≥ 4, the solution set is all real numbers greater than or equal to 4, represented as [4, ∞).

To find the solution to the compound inequality, we combine these two solution sets using the union (or) symbol:

(-∞, 10] ∪ [4, ∞)

So, in interval notation, the solution is (-∞, 10] ∪ [4, ∞).