Solve for x
x\in \begin{bmatrix}-\frac{5}{3},\frac{1}{2}\end{bmatrix}
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3x+5\geq 0 2x-1\leq 0
For the product to be ≤0, one of the values 3x+5 and 2x-1 has to be ≥0 and the other has to be ≤0. Consider the case when 3x+5\geq 0 and 2x-1\leq 0.
x\in \begin{bmatrix}-\frac{5}{3},\frac{1}{2}\end{bmatrix}
The solution satisfying both inequalities is x\in \left[-\frac{5}{3},\frac{1}{2}\right].
2x-1\geq 0 3x+5\leq 0
Consider the case when 3x+5\leq 0 and 2x-1\geq 0.
x\in \emptyset
This is false for any x.
x\in \begin{bmatrix}-\frac{5}{3},\frac{1}{2}\end{bmatrix}
The final solution is the union of the obtained solutions.
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