To solve the inequality \( 6x + 1 < 5x - 8 \), we can follow these steps:
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Subtract \(5x\) from both sides:
\[ 6x - 5x + 1 < -8 \]
This simplifies to:
\[ x + 1 < -8 \]
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Subtract 1 from both sides:
\[ x < -8 - 1 \]
So we have:
\[ x < -9 \]
Thus, the solution to the inequality \( 6x + 1 < 5x - 8 \) is:
\[ x < -9 \]