5 - x
______ ≥ 3 subtract 3 from both sides
4x + 1
5 - x
_____ - 3 ≥ 0 get a common denominator
4x + 1
5 - x - 3 ( 4x + 1)
_______________ ≥ 0
4x + 1
5 - x - 12x - 3
____________ ≥ 0
4x + 1
-13x + 2
_______ ≥ 0
4x + 1
We need to solve these two equations
-13x + 2 = 0 4x + 1 = 0
2 = 13x 4x = - 1
2/13 = x x = -1/4
We have three possible itervals that will solve the original equation
(-inf, -1/4 ) or ( -1/4, 2/13] or [ 2/13, inf)
If we pick an x value in (-1/4, 2/13] , say x =0, we find that
5 - 0 5
_______ = __ = 5 which makes the original inequality true
4(0) + 1 1
So....the solution is (-1/4, 2/13 ]