Question

The solution set for 6 < 2/3 m+2 is:

A. m < 3
B. m > 12
C. m < 7
D. m > 6

Answer 1

To find the solution set for the inequality 6 < 2/3 m + 2, we subtract 2 from both sides and then multiply by the reciprocal of 2/3, resulting in m > 6. Hence, the correct answer is D. m > 6.

Step-by-step explanation:

The solution set for 6 < 2/3 m + 2 can be found by isolating the variable m on one side of the inequality. Here's the step-by-step process:

1. Subtract 2 from both sides of the inequality: 6 - 2 < 2/3 m + 2 - 2, which simplifies to 4 < 2/3 m.
2. Multiply both sides by the reciprocal of 2/3 to isolate m: (3/2) × 4 < m, which simplifies to 6 < m.
3. Therefore, the final inequality representing the solution set is m > 6.

Hence, the correct answer is D. m > 6.