Question

Solve x-5=<6/x

Answer 1

-1 is less than or equal to x and x is less than 0

Answer 2

x-5=6/x
x(x-5)=6
x^2-5x-6=0
(x-6)(x+1)

x = 6 or x = -1

Answer 3

6x - 5 < 6/x

Step 1: Multiply everything by denominator (x).

6x - 5 < 6/x

x(6x - 5) < 6

6xˆ2 - 5x < 6

Step 2: Move all terms to one side of the inequality so that you'll get a polynomial that is less than zero.

6xˆ2 - 5x < 6

6xˆ2 - 5x - 6 < 0

Step 3: Factorize the polynomial.

6xˆ2 - 5x - 6 < 0

(3x + 2)(2x - 3) < 0

Step 4: Take each of the terms individually and set them to less than zero. Then Solve for "x".

First Term:

3x + 2 < 0

3x < -2

x < -2/3 (<==ANSWER!!)

Second Term:

2x - 3 < 0

2x < 3

x < 3/2 (<==ANSWER!!)


Therefore the answer to the inequality is

(-2/3) < x < (3/2)

***source*** yahoo.answers.com