Question

solve for the inequality: 3x-2/x-4 greater than or equal to 0... can anyone help?

Answer 1

You have two possibilities you have to take into consideration:

1. The numerator is greater than or equal to zero AND the denominator is greater than zero (it can't be zero).
2. The numerator is less than zero AND the denominator is less than zero.

So either:

3x - 2 >= 0 and x - 4 > 0
3x >= 2 and x > 4
x > = 2/3 and x > 4 which is only true when
x > 4

or:

3x - 2 < 0 and x - 4 < 0
3x < 2 and x < 4
x < 2/3 and x < 4 which is only true when
x < 2/3

So the answer is x < 2/3 and x > 4