Solve for x
x\in (-3,\frac{8}{3}]
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3x-8\geq 0 x+3<0
For the quotient to be ≤0, one of the values 3x-8 and x+3 has to be ≥0, the other has to be ≤0, and x+3 cannot be zero. Consider the case when 3x-8\geq 0 and x+3 is negative.
x\in \emptyset
This is false for any x.
3x-8\leq 0 x+3>0
Consider the case when 3x-8\leq 0 and x+3 is positive.
x\in (-3,\frac{8}{3}]
The solution satisfying both inequalities is x\in \left(-3,\frac{8}{3}\right].
x\in (-3,\frac{8}{3}]
The final solution is the union of the obtained solutions.
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