inequalities with less than or greater than symbol

Question

x-3/x+2 is greater than or equal to zero(0)

Answer 1

(x-3) / (x+2) >= 0

There are two points to consider:

x - 3 = 0 >> x = 3

x + 2 = 0 >> x = -2

Number line:

<-----(-2)-----(+3)----->

Let's try something to the left of -2:

(x-3)/(x+2) when x = -3

(-3-3)/(-3+2)

(-6)/(-1)

+1

1 is >= 0, so that section is in.

Let's try something between -2 and +3:

(x-3)/(x+2) when x = 0

(-3)/(+2)

-3/2

-3/2 is not >=0, so that section is out.

Let's try something to the right of +3:

(x-3)/(x+2) when x = 4

(4-3)/(4+2)

1/6

1/6 is >= 0, so that section is in.

Answer:  x <= -2 or x >= +3