Solve 2x-7/(x-5) < 3 inequality?

Question

This is an inequality problem with less than or equal to 3. Can you please help?
Here's the answer choices:

a) [8, positive infinity)
b) (negative infinity, 5)
c) (5,8]
d) (negative infinity,5) U [8, positive infinity)
e) None of the above

Please explain if you can.

Answer 1

answer d

wwefan you cnat't multiply both side of inequality by an expresion which consists of unknown. In this case you have to consider two cases:
x-5>0 and x-5<0. in the second case when multiplying you have to change the sign of the inequality.

Answer 2

the most to fixing any inequality with absolute values is to isolate absolutely the fee on one area, and then make 2 separate equations for both "values" (valuable and detrimental) of the inequality. enable me provide a normal party: |x-2| < 10 to remedy, you remedy those 2 inequalities: (x-2) < 10 and -(x-2) < 10 the answer should be both inequalities blended at the same time. in simple terms remember even as fixing both sides that once you multiply or divide both area of an inequality with assistance from a detrimental volume, you may change the route of the inequality.

Answer 3

Answer: A

how I got it:

2x-7<3(x-5)

2x-7<3x-15

2x+8<3x

8