For this inequality

Question

3x^(2) - 2x -1 > or equal 0

I get x=1 , x=-1/3

would the solution set become
{x|1 < x < -1/3}

I wasn't sure about the sign, if it should be greater than or equal to .

Answer 1

3x^2 - 2x - 1 >= 0,

Factor using the A*C Method:
A * C = 3 * -1 = -3 = 1 * -3,
3x^2 + (x -3x) - 1 >= 0,
(3x^2 - 3x) + (x - 1) >= 0,
3x(x - 1) + (x - 1) >= 0,
(x - 1) (3x + 1) >= 0,

x - 1 >= 0,
x >= 1.

3x + 1 >= 0,
3x >= -1,
x >= -1/3.

Solution Set: x >= 1, and x >= -1/3.

This is not a compound inequality; therefore, your last step does
not apply.