Peter
Lv 6
Peter asked in Science & MathematicsMathematics · 1 month ago

||3x + 8| / (2x - 3)| > 4?

How to solve the integer this inequation?

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  • Pope
    Lv 7
    1 month ago
    Favourite 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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