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Question

If |3x – 7| > 2, then x _______ 53 or, x _______ 3.

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Solution

|3x – 7| > 2
By defination of modulus inequality;
3x – 7 > 2 or 3x – 7 < –2
If 3x – 7 > 2
By adding 7 to both sides,
We get,
3x > 9
i.e. x > 9
If 3x – 7 < – 2
Now, by adding 7 to both sides,
We get,
3x – 7 + 7 < – 2 + 7
i.e. 3x < 5
i.e. x<53

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