Question

Which set of numbers is included in the solution set of 4−3x<−2?

A) {-8, 0, 1.5}
B) {0, 2.5, 8}
C) {-15, -8, 0}
D) {2.5, 8, 15}

Answer 1

To solve the inequality 4−3x<−2, subtract 4 from both sides and divide by -3. The set D) {2.5, 8, 15} is included in the solution set.

Step-by-step explanation:

To find the set of numbers included in the solution set of the inequality 4−3x<−2, we need to solve the inequality. We start by subtracting 4 from both sides of the inequality:

-3x < -6

Next, we divide both sides of the inequality by -3, remembering to reverse the inequality sign because we are dividing by a negative number:

x > 2

So, any numbers greater than 2 are included in the solution set. Looking at the answer choices, the set {2.5, 8, 15} is the only set that contains numbers greater than 2. Therefore, the correct answer is D) {2.5, 8, 15}.