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?

y <7H

Hy <7

y < 7 H

y < 7

1 answer

To solve the inequality \( Hy < 7 \), where \( H \) is a number greater than 0, you would divide both sides of the inequality by \( H \).

Starting with the original inequality:

\[ Hy < 7 \]

Divide both sides by \( H \) (which is positive, so the direction of the inequality does not change):

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

Since none of the provided options includes exactly that expression, let's analyze the given options.

The correct inequality derived from \( Hy < 7 \) should ultimately compare \( y \) to a constant. Given their proximity, the closest form from the options would represent this division.

However, if we want to re-express one of those options in terms of \( H \) being greater than 0, we can state:

  • Option: \( y < 7 H \) implies a multiplication, which is not quite the rearrangement we derived.
  • Option: \( Hy < 7 \) is just the original inequality.
  • Option: \( y < 7 H \) again implies a multiplication, incorrect for our purpose.
  • Option: \( y < 7 \) is not completely accurate without considering \( H \).

So, the concise solution reflecting \( y \) in terms of the constant division by \( H \) produces an effective conclusion that isn't listed directly among your choices, which can imply misunderstanding on variable placement or transformation.

Thus, the final solution indicates that:

  • The correct step is ultimately \( y < \frac{7}{H} \).

Ensure this is clear; neither is explicitly among your presented choices — reflect on dividing by \( H \) yields results emphasizing \( H \) must remain positive to maintain those integrity transformations throughout the line solution properly!