Solve for x
x\in (-\infty,-\frac{4}{5}]\cup [\frac{1}{2},\infty)
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-5x-4\geq 0 6x-3\leq 0
For the product to be ≤0, one of the values -5x-4 and 6x-3 has to be ≥0 and the other has to be ≤0. Consider the case when -5x-4\geq 0 and 6x-3\leq 0.
x\leq -\frac{4}{5}
The solution satisfying both inequalities is x\leq -\frac{4}{5}.
6x-3\geq 0 -5x-4\leq 0
Consider the case when -5x-4\leq 0 and 6x-3\geq 0.
x\geq \frac{1}{2}
The solution satisfying both inequalities is x\geq \frac{1}{2}.
x\geq \frac{1}{2}\text{; }x\leq -\frac{4}{5}
The final solution is the union of the obtained solutions.
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