Question

Solve: (x-1)/(x+3)>4

Answer 1

x-1=4(x+3), solve for x

Answer 2

x-1>4(x+3) ***

Answer 3

oops beware!

Answer 4

-13/3 < x < -3

Answer 5

it might be easier to see when written as (x-1)/(x+3) = 1 + (-4)/(x+3) > 4 so that values of x less than -3 but close enough will work

Answer 6

(x-1)/(x+3) - 4 > 0
(x-1)/(x+3) - 4(x+3)/(x+3) > 0
(x-1-4x-12) / (x+3) > 0
(-3x -13) / (x+3) > 0
x cant be -3 because it will make the denominator zero.
then plug any value of x :
* between -3 and -13/3 (the value of the left side will be positiive)
*larger than -3 (the value of the left side will be negative)
*and smaller than -13/3. (the value of the left side will be negative
since (-3x -13) / (x+3) > 0 , we need the value of the left side to be positive.
therefore the solution is -13/3 < x < -3

Answer 7

Thank you!