B1. Find all real numbers $a \geq 0$ for which the equation $2|x-a|+3|x+a|=1$ has at least one real solution.
B1. Let's consider several possibilities. If $x > a$, we get $2(x-a)+3(x+a)=1$ or $x=\frac{1-a}{5}$. For this to be a solution, it must hold that $\frac{1-a}{5} > a$ or $a < \frac{1}{6} \ldots \ldots \ldots \ldots \ldots \ldots$.

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