To solve the inequality \( 4y + 1 > 17 \), we first isolate \( y \):
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Subtract 1 from both sides: \[ 4y > 16 \]
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Divide both sides by 4: \[ y > 4 \]
Now, to express the solution in set notation, we write:
\[ { y \in \mathbb{R} \mid y > 4 } \]
This means "the set of all \( y \) in the real numbers such that \( y \) is greater than 4."