Solve for a
a\in [-\frac{1}{2},0)
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\frac{2a+1}{2a}\leq 0
Divide both sides by -1. Since -1 is negative, the inequality direction is changed. Zero divided by any non-zero number gives zero.
2a+1\geq 0 2a<0
For the quotient to be ≤0, one of the values 2a+1 and 2a has to be ≥0, the other has to be ≤0, and 2a cannot be zero. Consider the case when 2a+1\geq 0 and 2a is negative.
a\in [-\frac{1}{2},0)
The solution satisfying both inequalities is a\in \left[-\frac{1}{2},0\right).
2a+1\leq 0 2a>0
Consider the case when 2a+1\leq 0 and 2a is positive.
a\in \emptyset
This is false for any a.
a\in [-\frac{1}{2},0)
The final solution is the union of the obtained solutions.
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