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Solve the inequality: `x^2 + 2x - 24 >= 0`

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lkballer24 | Student, Grade 11 | Valedictorian

Posted August 21, 2013 at 4:04 PM via web

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Solve the inequality: `x^2 + 2x - 24 >= 0`

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted August 21, 2013 at 4:46 PM (Answer #1)

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The inequality `x^2 + 2x - 24 >= 0` has to be solved.

x^2 + 2x - 24 `>=` 0

=> x^2 + 6x - 4x - 24 `>=` 0

=> x(x + 6) - 4(x + 6) `>=` 0

=> (x - 4)(x + 6) `>=` 0

This is the case when x - 4 `>=` 0 and x + 6 `>=` 0

=> x `>=` 4 and x `>=` -6

=> x `>=` 4

And when x `<=` 4 and x `<=` -6

=> x `<=` 4 and x `<=` -6

=> x `<=` -6

The solution of the inequality is x `>=` 4, x `<=` -6

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