Question

which inequality is equivalent to x-6/x+5≥x+7/x+3?

Answer 1

To find equivalent inequalities you have to work the inequality given.

The first step is transpose on of sides to have an expression in one side and zero in the other side:

  x - 6        x + 7
--------- ≥  --------
  x + 5       x + 3

=>

  x - 6          x + 7
--------- -  --------   ≥ 0
  x + 5       x + 3

=>

 (x - 6) (x + 3) - (x + 7) (x + 5)
--------------------------------------- ≥ 0
          (x + 5) (x + 3)

=>

 x^2 - 3x - 18 - x^2 - 12x - 35
--------------------------------------- ≥ 0
         (x + 5) (x + 3)

           15x + 53
-     -------------------   ≥ 0
       (x + 5) (x + 3)

That is an equivalent inequality. Sure you can arrange it to find many other equivalent inequalities. That is why you should include the list of choices. Anyway from this point it should be pretty straigth to arrange the terms until making the equivalent as per the options.

Answer 2

In this exercise we want to know if the inequality are equivalent so we have to:

That is an equivalent inequality.

What is a equivalent inequality ?

Two or more inequalities that have the same truth set with respect to the same universe set are called equivalent inequalities, so the two inequalities are equivalent.

Then we have the two inequalities as:

$x - 6/ x + 5 \geq x + 7/x + 3\\(x - 6 / x + 5) - (x + 7/x + 3)\geq 0\\(x - 6)*(x + 3) - (x + 7)*(x + 5)/ [ (x + 5)* (x + 3)] \geq 0\\ x^2 - 3x - 18 - x^2 - 12x - 35/ (x + 5) (x + 3) \geq 0\\- 15x + 53/ (x + 5) (x + 3)\geq 0$

See more about inequality at  brainly.com/question/19491153