Solve for x
x\in \begin{bmatrix}-\frac{5}{3},7\end{bmatrix}
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3x+5\leq 0 7-x\leq 0
For the product to be ≥0, 3x+5 and 7-x have to be both ≤0 or both ≥0. Consider the case when 3x+5 and 7-x are both ≤0.
x\in \emptyset
This is false for any x.
7-x\geq 0 3x+5\geq 0
Consider the case when 3x+5 and 7-x are both ≥0.
x\in \begin{bmatrix}-\frac{5}{3},7\end{bmatrix}
The solution satisfying both inequalities is x\in \left[-\frac{5}{3},7\right].
x\in \begin{bmatrix}-\frac{5}{3},7\end{bmatrix}
The final solution is the union of the obtained solutions.
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