Solve for x
x\in (-1,2]
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x-2\geq 0 x+1<0
For the quotient to be ≤0, one of the values x-2 and x+1 has to be ≥0, the other has to be ≤0, and x+1 cannot be zero. Consider the case when x-2\geq 0 and x+1 is negative.
x\in \emptyset
This is false for any x.
x-2\leq 0 x+1>0
Consider the case when x-2\leq 0 and x+1 is positive.
x\in (-1,2]
The solution satisfying both inequalities is x\in \left(-1,2\right].
x\in (-1,2]
The final solution is the union of the obtained solutions.
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