Yahoo Answers: Answers and Comments for 3x + 8 / (2x  3) > 4? [Mathematics]
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From Peter
enMY
Sun, 23 Feb 2020 09:04:36 +0000
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Yahoo Answers: Answers and Comments for 3x + 8 / (2x  3) > 4? [Mathematics]
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From Pope: Both sides of the inequality are nonnegative,...
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https://malaysia.answers.yahoo.com/question/index?qid=20200223090436AAFGB9M
Sun, 23 Feb 2020 09:52:46 +0000
Both sides of the inequality are nonnegative, so feel free to square both sides with impunity.
3x + 8 / (2x  3) > 4
(3x + 8)² / (2x  3)² > 16
(3x + 8)² > 16(2x  3)² ... multiplication by a positive
(3x + 8)²  16(2x  3)² > 0
[(3x + 8) + 4(2x  3)][(3x + 8)  4(2x  3)] > 0
(11x  4)(5x + 20) > 0
(11x  4)(x  4) < 0 ... division by (5)
4/11 < x < 4 and x ≠ 3/2
4/11 < x < 3/2 or 3/2 < x < 4
Set of integer solutions: {1, 2, 3}