What is the value of x for which (2x - 12)(5 - 3x) < 0

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The values of x that satisfy (2x - 12)(5 - 3x) < 0 are those where either:

  • 2x - 12 < 0 and 5 - 3x > 0

=> 2x < 12 and 5 > 3x

=> x < 6 and x < 5/3

=> x < 5/3

  • 2x - 12 > 0 and 5 - 3x < 0

=> 2x > 12 and 5 < 3x

=> x > 6 and x > 5/3

=> x > 6

The solution of the given inequality is `(-oo, 5/3)U(6, oo)`