[tex]\frac{3x-1}{2} -\frac{2x+1}{5} \leq \frac{x+1}{10} |*10\\5(3x-1)-2(2x+1)\leq x+1\\15x-5-4x-2-x\leq 1 \\10x\leq 1+7\\10x\leq 8|:10\\x\leq \frac{4}{5} \\x\in (-\infty ; \frac{4}{5} ][/tex]
[tex]2x-\frac{x-1}{4} < \frac{3x-1}{2} +x|*4\\8x-(x-1) < 2(3x-1)+4x\\8x-x+1 < 6x-2+4x\\7x-10x < -2-1\\-3x < -3|:(-3) \\x > 1\\x \in (1; \infty)[/tex]
[tex]\frac{2x+1}{4} -x\geq \frac{1-x}{2} |*4\\2x+1-x\geq 2(1-x)\\x+1\geq 2-2x\\x+2x\geq 2-1\\3x\geq 1|:3\\x\geq \frac{1}{3} \\x\in [\frac{1}{3} ;\infty)[/tex]
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[tex]\frac{3x-1}{2} -\frac{2x+1}{5} \leq \frac{x+1}{10} |*10\\5(3x-1)-2(2x+1)\leq x+1\\15x-5-4x-2-x\leq 1 \\10x\leq 1+7\\10x\leq 8|:10\\x\leq \frac{4}{5} \\x\in (-\infty ; \frac{4}{5} ][/tex]
[tex]2x-\frac{x-1}{4} < \frac{3x-1}{2} +x|*4\\8x-(x-1) < 2(3x-1)+4x\\8x-x+1 < 6x-2+4x\\7x-10x < -2-1\\-3x < -3|:(-3) \\x > 1\\x \in (1; \infty)[/tex]
[tex]\frac{2x+1}{4} -x\geq \frac{1-x}{2} |*4\\2x+1-x\geq 2(1-x)\\x+1\geq 2-2x\\x+2x\geq 2-1\\3x\geq 1|:3\\x\geq \frac{1}{3} \\x\in [\frac{1}{3} ;\infty)[/tex]