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Solve the given inequality for real x: 3x – 7 > 5x – 1.

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Solve the given inequality for real x: 3x – 7 > 5x – 1
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3x – 7 > 5x – 1
⇒ 3x – 7 + 7 > 5x – 1 + 7
⇒ 3x > 5x + 6
⇒ 3x – 5x > 5x + 6 – 5x
⇒ – 2x > 6

Thus, all real numbers x, which are less than  3, are the solutions of the given inequality.
Hence, the solution set of the given inequality is (–∞, –3).

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