How do you solve #x- 4\geq \frac { 8} { x - 2}#?

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Answer 1 · 2017-08-21T16:01:06

#[0,2)uu(2,oo)# or #0<=x<2# and #x>=6# (Both are the same, just in different notation)

Multiply both sides by #x-2# to isolate the nasty fraction on the RHS.

#(x-4)(x-2)>=8#

Expand

#x^2-6x+8>=8#

Subtract #8# from both sides

#x^2-6x>=0#

Solve the quadratic. You can use the Quadratic Formula, but I will just solve by factorising since it is the quickest.

#x(x-6)>=0#

#x>=0, x>=6#

Now note that in the original equation, #x=2# is undefined because the denominator equals #0#.

Therefore we have a new interval - #[0,2)uu(6,oo)# which is also the same as #0<=x<2# and #x>=6#
And that is our answer.