Question

Which of the following shows how to solve the linear inequality with a letter coefficient Hy < 7, where H is a number greater than 0?
A. y < 7/H
B. y < 7
C. Hy < 7
D. y < 7H

Answer 1

are you sure this is correct

Answer 2

To solve the linear inequality \( Hy < 7 \) for \( y \), where \( H \) is a number greater than 0, we can isolate \( y \) by dividing both sides of the inequality by \( H \).

Starting with:
\[ Hy < 7 \]

Now, divide both sides by \( H \):
\[ y < \frac{7}{H} \]

Thus, the correct choice is:
**A. \( y < \frac{7}{H} \)**.

Answer 3

Yes, I am confident that the solution is correct. Let's break it down step by step:

We start with the inequality:

\[ Hy < 7 \]

Since \( H > 0 \), we can safely divide both sides of the inequality by \( H \) without changing the inequality's direction. So we divide:

\[ y < \frac{7}{H} \]

This leads us to the conclusion that:

**The correct answer is A: \( y < \frac{7}{H} \)**.

If \( H \) were negative, we would have to reverse the inequality, but since \( H \) is stated to be greater than 0, the direction of the inequality stays the same. Therefore, the solution is valid as stated.