Question

Which of the following sets shows all the numbers from the set ( ) that are part of the solution to the inequality 7x + 6 > 20?

A. {3, 4}
B. {1, 2, 3}
C. {3, 4, 5}
D. {2, 3, 4}

Answer 1

To solve the inequality 7x + 6 > 20, subtract 6 and divide by 7 to get x > 2. The correct set that includes all numbers greater than 2 is Set A, which is {3, 4}.

Step-by-step explanation:

To solve the inequality 7x + 6 > 20, we first isolate the variable x.

1. Subtract 6 from both sides to get 7x > 14.
2. Divide both sides by 7 to get x > 2.

This means that the solution set includes all numbers greater than 2. Looking at the sets provided:

• Set A: {3, 4} includes numbers greater than 2.
• Set B: {1, 2, 3} includes numbers not strictly greater than 2 (1 and 2 are not solutions).
• Set C: {3, 4, 5} includes numbers greater than 2.
• Set D: {2, 3, 4} includes the number 2, which is not strictly greater than 2 (not a solution).

Only Set A ({3, 4}) and Set C ({3, 4, 5}) include only numbers that are part of the solution to the inequality. However, the question asks for all numbers from the set that are part of the solution; hence, Set C includes numbers not listed in the question prompt. Thus, the correct answer is Set A.