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$1)\; \; (2x-3)(x+1) \geq 0\\\\+++[\, -1\, ]---[\frac{3}{2}\, ]+++\\\\x\in (-\infty ,-1\, ]\cup [\, \frac{3}{2} ,+\infty )\\\\2)\; \; 4x^2+4x-3 \leq 0\\\\D/4=4+12=16\\\\x_1=\frac{-2-4}{4}=-\frac{3}{2}\; ,\; \; x_2=\frac{-2+4}{4}=\frac{1}{2}\\\\4(x+\frac{3}{2})(x-\frac{1}{2}) \leq 0\\\\+++[-\frac{3}{2}\, ]---[\, \frac{1}{2}\, ]+++\\\\x\in [-\frac{3}{2},\frac{1}{2}\, ]$

$3)\; \; y=\sqrt{6x-x^2}+3\sqrt[4]{2x-5}\\\\OOF:\; \; \left \{ {{6x-x^2 \geq 0} \atop {2x-5 \geq 0}} \right. \; \left \{ {x(6-x) \geq 0} \atop {2x-5 \geq 0}} \right. \; \left \{ {{x(x-6) \leq 0} \atop {x \geq \frac{5}{2}}} \right. \; \left \{ {{0 \leq x \leq 6} \atop {x \geq 2,5}} \right. \\\\-----[0]/////////////////[6]-----\\--------[2,5]//////////////////////\\\\x\in [\, 2,5\; ;\; 6\, ]$