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Question Number 201820 by cortano12 last updated on 13/Dec/23

$$\frac{\mid 3\mathrm{x}+1\mid -\mid \mathrm{x}+2\mid }{3-\mid 2\mathrm{x}\mid }⩾0$$$$\mathrm{find}\mathrm{the}\mathrm{solution}\mathrm{set}.$$

Answered by dimentri last updated on 13/Dec/23

$$\frac{{(3\mathrm{x}+1)}^2-{(\mathrm{x}+2)}^2}{3^2-{\left(2\mathrm{x}\right)}^2}⩾0$$$$\frac{(4\mathrm{x}+3)(2\mathrm{x}-1)}{(3+2\mathrm{x})(3-2\mathrm{x})}⩾0$$$$-\frac{3}{2}<\mathrm{x}⩽-\frac{3}{4}\vee \frac{1}{2}⩽\mathrm{x}<\frac{3}{2}$$

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