Question

(x+8)/(x-2)≥0 please solve the inequality for the value of x step by step explanation

Answer 1

Answer:

        x > 2  or  x ≤ -8

Step-by-step explanation:

For a fraction a/b to be positive, both a and b have to have the same sign, either both positive or both negative.  Also, in such a fraction, b≠0.

So...

    (x + 8) / (x - 2)  ≥  0

⇔  either  [ x+8 ≥ 0  and  x-2 > 0 ]  or  [ x+8 ≤ 0  and  x-2 < 0 ]

⇔  either  [ x ≥ -8  and  x > 2 ]  or  [ x ≤ -8  and  x < 2 ]

⇔  either  x > 2  or  x ≤ -8.