To solve the inequality \(-7(x + 1) > -9 - 5x\), follow these steps:
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Distribute \(-7\) on the left side: \[ -7x - 7 > -9 - 5x \]
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Move the \(5x\) term from the right side to the left side: \[ -7x + 5x - 7 > -9 \] This simplifies to: \[ -2x - 7 > -9 \]
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Next, add \(7\) to both sides: \[ -2x > -2 \]
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Divide each side by \(-2\). Remember, when you divide or multiply by a negative number, you must flip the inequality sign: \[ x < 1 \]
Thus, the solution to the inequality is: \[ \boxed{x < 1} \]