Final answer:
After analyzing the given inequalities and transforming each to solve for 'y', none of them define an inequality with a solution where values are greater than or equal to -4. Therefore, the correct answer is d. None of the above.
Step-by-step explanation:
The student is asking to define an inequality that has a solution set where the values are greater than or equal to -4. To analyze this, let's look at the inequalities presented and check if they fit this criterion when transforming each inequality to solve for 'y'.
- a. -2x + 3y - 5 < -4 simplifies to 3y > -2x - 1, which does not define y as being greater than or equal to -4.
- b. 2x + 3y - 5 > -4 rearranges to 3y > -2x + 1, which also does not define y as being greater than or equal to -4.
- c. -2x - 3y + 5 ≤ 4 can be transformed into -3y ≤ -2x - 1, and after dividing by -3 (which reverses the inequality sign), we get y ≥ 2x/3 + 1/3. This still does not constitute an inequality with a solution of y ≥ -4 only.
Since none of the options directly define an inequality with a solution of greater than or equal to -4, the correct answer is d. None of the above.