To solve the inequality \(-6(w + 1) < 2(w + 5)\), we will first distribute the terms on both sides.
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Distribute \(-6\) on the left side: \[ -6w - 6 < 2(w + 5) \]
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Distribute \(2\) on the right side: \[ -6w - 6 < 2w + 10 \]
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Now, we can rearrange the inequality to get all \(w\) terms on one side and the constant terms on the other side. First, add \(6w\) to both sides: \[ -6 < 2w + 6w + 10 \] \[ -6 < 8w + 10 \]
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Next, subtract \(10\) from both sides: \[ -6 - 10 < 8w \] \[ -16 < 8w \]
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Now, divide both sides by \(8\): \[ \frac{-16}{8} < w \] \[ -2 < w \]
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This can also be written as: \[ w > -2 \]
Therefore, the solution to the inequality \(-6(w + 1) < 2(w + 5)\) is:
\[ w > -2 \]