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- PopeLv 71 month agoFavourite answer
Both sides of the inequality are non-negative, 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}

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