To solve the inequality \(-7(x + 1) > -9 - 5x\), we will follow these steps:
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Distribute \(-7\) on the left side: \[ -7x - 7 > -9 - 5x \]
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Next, we will get all terms involving \(x\) on one side and constant terms on the other side. To do this, add \(7x\) to both sides: \[ -7 > -9 + 2x \]
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Now, isolate \(2x\) by adding \(9\) to both sides: \[ 2 > 2x \]
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Divide both sides by \(2\): \[ 1 > x \]
This can also be written as: \[ x < 1 \]
Thus, the solution to the inequality \(-7(x + 1) > -9 - 5x\) is: \[ x < 1 \]