Question

2x+5/2>3/2x-2

Answer 1

By the way, you should write it like this:

(2x + 5)/2 > 3/(2x - 2)

This is so that people don't mis-interpret the fractions

Answer 2

Hi Hero, that's how the book showed it

Answer 3

You want people to read it as \(\large\frac{2x + 5}{2} > \frac{3}{2x -2}\)

not as \(2x + \frac{5}{2} > \frac{3}{2x} - 2\)

Answer 4

Do you see how it can be mis-interpreted as such?

Answer 5

to tell you the truth all of this really has my head spinning....:( With your example I can see the difference. Thank you for breaking it down for me

Answer 6

So anyway, getting to the inequality, we know that x ≠ 1 because that would result in a zero denominator.

Answer 7

Now cross multiply and then solve the inequality:

(2x + 5)(2x - 2) > (2)(3)
2x(2x - 2) + 5(2x - 2) > 6
4x^2 - 4x + 10x - 10 > 6
4x^2 + 10x - 4x - 10 > 6
4x^2 + (10 - 4)x - 10 > 6
4x^2 + 6x - 10 > 6
4x^2 + 6x - 10 - 6 > 0
4x^2 + 6x - 16 > 0
2(2x^2 + 3x - 8) > 0
2x^2 + 3x - 8 > 0

(-2.886,1),(1.386, infinity)

Answer 8

Thanks so much for the break down and answer. I understand it a lot more now.