Ответ: x=-1.

Объяснение:

[tex]\displaystyle\\\left \{ {{\frac{3x+2}{2}-2\geq 4x\ |*2 } \atop {(x+5)(x-3)\geq x(x-1)-19}} \right. \ \ \ \ \left \{ {{3x+2-4\geq 8x} \atop {x^2+5x-3x-15\geq x^2-x-19}} \right. \\\\\\\\\left \{ {{-2\geq 5x\ |:5} \atop {2x-15\geq -x-19}} \right.\ \ \ \ \left \{ {{-0,4\geq x} \atop {3x\geq -4\ |:3}} \right. \ \ \ \ \left \{ {{x\leq -0,4} \atop {x\geq -\frac{4}{3} }} \right. \ \ \ \ \left \{ {{x\leq -\frac{2}{5} } \atop {x\geq -1\frac{1}{3} }} \right.\ \ \ \ \Rightarrow\\\\\\[/tex]

                     [tex]-1\frac{1}{3} \leq x\leq -\frac{2}{5} \ \ \ \ \Rightarrow\ \ \ \ x=-1.[/tex]