$$x \geq \frac{ x-1 }{ 3 } - \frac{ x+3 }{ 2 }$$
$x\geq -\frac{11}{7}$
$$x\geq \frac{2\left(x-1\right)}{6}-\frac{3\left(x+3\right)}{6}$$
$$x\geq \frac{2\left(x-1\right)-3\left(x+3\right)}{6}$$
$$x\geq \frac{2x-2-3x-9}{6}$$
$$x\geq \frac{-x-11}{6}$$
$$x\geq -\frac{1}{6}x-\frac{11}{6}$$
$$x+\frac{1}{6}x\geq -\frac{11}{6}$$
$$\frac{7}{6}x\geq -\frac{11}{6}$$
$$x\geq -\frac{11}{6}\times \frac{6}{7}$$
$$x\geq \frac{-11\times 6}{6\times 7}$$
$$x\geq \frac{-11}{7}$$
$$x\geq -\frac{11}{7}$$
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