[tex]\left \{ {{\frac{1-x}{4}\geq \frac{5-x}{2} } \atop {(2x-1)^2-6 > (2x-3)(2x+3)}} \right. \\\\\left \{ {{1-x\geq 10-2x} \atop {4x^2-4x+1-6 > 4x^2-9}} \right. \\\\\left \{ {{x\geq 9} \atop {-4x > -4}} \right. \\\\\left \{ {{x\geq 9} \atop {x < 1}} \right. \\\\\\[/tex]
x∈(-∞,1)∪<9,+∞)
[tex]\left \{ {{(x+1)^2+7 < (x-4)^2} \atop {(1+x)^2+3x^2 > (2x-1)^2-3}} \right. \\\\\left \{ {{x^2+2x+1+7 < x^2-8x+16} \atop {1+2x+x^1+3x^2 > 4x^2-4x+1-3}} \right. \\\\\left \{ {{10x < 8} \atop {6x > -3}} \right. \\\\\left \{ {{x < \frac{4}{5} } \atop {x > -\frac{1}{2} }} \right. \\\\[/tex]
x∈[tex](-\frac{1}{2},\frac{4}{5})[/tex]
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[tex]\left \{ {{\frac{1-x}{4}\geq \frac{5-x}{2} } \atop {(2x-1)^2-6 > (2x-3)(2x+3)}} \right. \\\\\left \{ {{1-x\geq 10-2x} \atop {4x^2-4x+1-6 > 4x^2-9}} \right. \\\\\left \{ {{x\geq 9} \atop {-4x > -4}} \right. \\\\\left \{ {{x\geq 9} \atop {x < 1}} \right. \\\\\\[/tex]
x∈(-∞,1)∪<9,+∞)
[tex]\left \{ {{(x+1)^2+7 < (x-4)^2} \atop {(1+x)^2+3x^2 > (2x-1)^2-3}} \right. \\\\\left \{ {{x^2+2x+1+7 < x^2-8x+16} \atop {1+2x+x^1+3x^2 > 4x^2-4x+1-3}} \right. \\\\\left \{ {{10x < 8} \atop {6x > -3}} \right. \\\\\left \{ {{x < \frac{4}{5} } \atop {x > -\frac{1}{2} }} \right. \\\\[/tex]
x∈[tex](-\frac{1}{2},\frac{4}{5})[/tex]