[tex](3x+23)^{2}\geq 4(x-23)^{2}\\9x^{2} +138x+529\geq 4(x^{2} -46x+529)\\9x^{2} +138x+529\geq 4x^{2} -184x+2116\\9x^{2} +138x+529-4x^{2} +184x-2116\geq 0\\5x^{2} +322x-1587\geq 0\\5x^{2} +345x-23x-1587\geq 0\\5x*(x+69)-23(x+69)\geq 0\\(x+69)*(5x-23)\geq 0\\\left \{ {{x+69\geq 0} \atop {5x-23\geq 0}} \right.\\\left \{ {{x+69\leq 0} \atop {5x-23\leq 0}} \right.\\\left \{ {{x\geq-69} \atop {x\geq \frac{23}{5} }} \right.\\\left \{ {{x\leq -69} \atop {x\leq \frac{23}{5} }} \right.\\[/tex]
x∈[[tex]\frac{23}{5}[/tex],+∞>
x∈<-∞,-69]
x∈<-∞,-69]∪[[tex]\frac{23}{5}[/tex],+∞>
