Answer to Question #37102 in Algebra for Sadaam Ahmed

Question

Solve l x / x - 4l ≥ 1.

Answer 1

As we know: lx /x - 4l=lxl/lx - 4l
1) Assume x<0 ==> lxl/lx - 4l=-x/(-x+4), so we have -x/(4-x)≥1 ==> -x≥4-x ==> 0≥4 impossible so x<0 is not a solution
2) Assume 0<=x<4 ==> lxl/lx - 4l=x/(4-x), so we have x/(4-x)≥1 ==> x≥4-x ==> x≥2
3) Assume x≥4 ==> lxl/lx - 4l=x/(x-4), so we have x/(x-4)≥1 ==> x≥x-4 ==> 0≥-4 is true for all x≥4
From 2) and 3) we have that the solution of our inequation is: x≥2