Solve for x
x\in (-\infty,\frac{3}{4})\cup [1,\infty)
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1-x\geq 0 4x-3<0
For the quotient to be ≤0, one of the values 1-x and 4x-3 has to be ≥0, the other has to be ≤0, and 4x-3 cannot be zero. Consider the case when 1-x\geq 0 and 4x-3 is negative.
x<\frac{3}{4}
The solution satisfying both inequalities is x<\frac{3}{4}.
1-x\leq 0 4x-3>0
Consider the case when 1-x\leq 0 and 4x-3 is positive.
x\geq 1
The solution satisfying both inequalities is x\geq 1.
x<\frac{3}{4}\text{; }x\geq 1
The final solution is the union of the obtained solutions.
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