Question

Which of the following sets shows all the numbers from the set {1, 2, 3, 4} that are part of the solution to the inequality 7x + 6 > 20?

A) {1, 2, 3}
B) {2, 3, 4}
C) {3, 4}
D) {4}

Answer 1

To find the numbers from the set {1, 2, 3, 4} that are part of the solution to the inequality 7x + 6 > 20, we need to substitute each number from the set into the inequality and check if it is true or false. The numbers that satisfy the inequality are 3 and 4.

Step-by-step explanation:

To find the numbers from the set {1, 2, 3, 4} that are part of the solution to the inequality 7x + 6 > 20, we need to substitute each number from the set into the inequality and check if it is true or false. Let's do this for each number:

1. For x = 1: 7(1) + 6 > 20 --> 7 + 6 > 20 --> 13 > 20 (False)
2. For x = 2: 7(2) + 6 > 20 --> 14 + 6 > 20 --> 20 > 20 (False)
3. For x = 3: 7(3) + 6 > 20 --> 21 + 6 > 20 --> 27 > 20 (True)
4. For x = 4: 7(4) + 6 > 20 --> 28 + 6 > 20 --> 34 > 20 (True)

Therefore, the numbers that satisfy the inequality are 3 and 4. The set that represents this is {3, 4}. So, the correct answer is C) {3, 4}.