Question
You solved the associated equation for
-10z
> -30 and found that the boundary point for this inequality is z = 3. Now, you are trying to figure out if the boundary point of z = 3 is included in solutions to the inequality. Is 3 also a solution to the inequality?
-10z
> -30
-10z
= -30
z = 3
Yes
No
-10z
> -30 and found that the boundary point for this inequality is z = 3. Now, you are trying to figure out if the boundary point of z = 3 is included in solutions to the inequality. Is 3 also a solution to the inequality?
-10z
> -30
-10z
= -30
z = 3
Yes
No
Answers
GPT-4o mini
To determine whether the boundary point \( z = 3 \) is included in the solutions to the inequality \( -10z > -30 \), we should first consider what the boundary point \( z = 3 \) represents.
The equation \( -10z = -30 \) simplifies to \( z = 3 \), which is the point where the inequality changes from true to false.
Since the original inequality is strict (using "greater than" rather than "greater than or equal to"), the boundary point itself (3) does not satisfy the inequality.
So the answer is **No**, \( z = 3 \) is not a solution to the inequality \( -10z > -30 \).
The equation \( -10z = -30 \) simplifies to \( z = 3 \), which is the point where the inequality changes from true to false.
Since the original inequality is strict (using "greater than" rather than "greater than or equal to"), the boundary point itself (3) does not satisfy the inequality.
So the answer is **No**, \( z = 3 \) is not a solution to the inequality \( -10z > -30 \).