What is the solution of the inequality 3x^2 - 2x - 5 >= 0

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The solution of the inequality `3x^2 - 2x - 5 >= 0` has to be determined.

`3x^2 - 2x - 5 >= 0`

Factor the left hand side.

`3x^2 - 5x + 3x - 5 >= 0`

=> `x(3x - 5) + 1(3x - 5) >= 0`

=> `(x + 1)(3x - 5) >= 0`

This is true if either `x + 1 >= 0` and `3x - 5 >= 0` or if `x + 1 <= 0` and `3x - 5 <= 0`

`x + 1 >= 0` and `3x - 5 >= 0`

=> `x >= -1` and `x >= 5/3`

=> `x >= 5/3`

`x + 1 <= 0` and `3x - 5 <= 0`

=> `x <= -1` and `x <= 5/3`

=> `x <= -1`

The value of x that satisfies the equation lies in the set `(-oo, -1]U[5/3, oo)` 

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