How do you solve #\frac { x - 1} { x - 2} - 3\geq 0#?
2 Answers
Update: x could be any real number but
Explanation:
First off,
So,
Then add 3 on both sides,
Multiply both sides by
Distribute
Combine like terms
Divide by 2 on both sides
So
However since you do not know if
Therefore you could have
So really x could equal any number except for 2.
Thanks George C.!
Explanation:
Given:
#(x-1)/(x-2)-3 >= 0#
First combine the rational expression with the constant
#((x-1)-3(x-2))/(x-2) >= 0#
That is:
#(-2x+5)/(x-2) >= 0#
In order that the left hand side be non-negative, we need one of the following:
-
#-2x+5 >= 0# and#x-2 > 0# . Hence#x in (-oo, 5/2] nn (2, oo) = (2, 5/2]# -
#-2x+5 <= 0# and#x-2 < 0# . Hence#x in [5/2, oo) nn (-oo, 2) = O/#
graph{(-2x+5)/(x-2) [-10, 10, -5, 5]}