Question

What interval includes all possible values of x, where (3(6 - 2x) ≤ 24x + 12)?

(A) (-[infinity], -3]
(B) (-3, 0)
(C) (-[infinity], 15)
(D) [15, [infinity])

Answer 1

The interval that includes all possible values of x, where (3(6 - 2x) ≤ 24x + 12), is [1/5, ∞). So, the interval that includes all possible values of x is [1/5, ∞).

Step-by-step explanation:

To find the interval that includes all possible values of x, we need to solve the inequality.

Let's start by simplifying both sides.

3(6 - 2x) ≤ 24x + 12

18 - 6x ≤ 24x + 12

18 - 12 ≤ 24x + 6x

6 ≤ 30x

x ≥ 6/30 or x ≥ 1/5

So, the interval that includes all possible values of x is [1/5, ∞).