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)`

## We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

- 30,000+ book summaries
- 20% study tools discount
- Ad-free content
- PDF downloads
- 300,000+ answers
- 5-star customer support

Already a member? Log in here.

Are you a teacher? Sign up now