To solve the inequality \( 6x + 9 > 57 \), follow these steps:
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Subtract 9 from both sides:
\[ 6x + 9 - 9 > 57 - 9 \]
This simplifies to:
\[ 6x > 48 \]
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Now, divide both sides by 6:
\[ \frac{6x}{6} > \frac{48}{6} \]
This simplifies to:
\[ x > 8 \]
So, the solution to the inequality is:
\[ x > 8 \]