Solve the inequality x^2-5x-24<0

Question

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Answer 1

 

The inequality x^2-5x-24<0 has to be solved.

x^2-5x-24<0

=> x^2 - 8x + 3x - 24 < 0

=> x(x -8) + 3(x - 8) < 0

=> (x + 3)(x - 8) < 0

This is possible when either of the following are true:

• x + 3 < 0 and x -8 > 0

=> x < -3 and x > 8

This is not possible

• x + 3 > 0 and x - 8 < 0

=> x > -3 and x < 8

x in (-3, 8)

The solution of the inequality is the set (-3, 8)

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