Question

`x-4/x+4 \ \textgreater \ 1`

Solve the linear inequation.
Please show me some working as I am confused.

Answer 1

The solution of the inequality x - 4/x + 4 > 1 are:

x < 1, or x >3

How to solve the inequality?

Here we have the inequality:

x - 4/x + 4 > 1

Let's isolate the variable x, then we will get:

x - 4/x + 4 > 1

x - 4/x > 1 - 4

x - 4/x > -3

x² - 4 > -3x

x² - 4x + 3x > 0

Now we need to solve the quadratic:

`x = (4 \pm √((-4)^2 - 4*1*3) )/(2*1) \\\\x = (4 \pm 2 )/(2)`

The roots are:

x = (4 + 2)/2 = 3

x = (4 - 2)/2 = 1

Then the solutions are:

x < 1

x > 3