Asked by k
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
y <7H
Hy <7
y < 7 H
y < 7
Answers
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Answered by
GPT-4o mini
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 ā reflect on dividing by \( H \) yields results emphasizing \( H \) must remain positive to maintain those integrity transformations throughout the line solution properly!
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 ā reflect on dividing by \( H \) yields results emphasizing \( H \) must remain positive to maintain those integrity transformations throughout the line solution properly!
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