Solve for x
x\in \mathrm{R}
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6-3x\geq 0 x-2\leq 0
For the product to be ≤0, one of the values 6-3x and x-2 has to be ≥0 and the other has to be ≤0. Consider the case when 6-3x\geq 0 and x-2\leq 0.
x\leq 2
The solution satisfying both inequalities is x\leq 2.
x-2\geq 0 6-3x\leq 0
Consider the case when 6-3x\leq 0 and x-2\geq 0.
x\geq 2
The solution satisfying both inequalities is x\geq 2.
x\in \mathrm{R}
The final solution is the union of the obtained solutions.
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