Получаем 3 промежутка:
![\left(-\infty;\;-\frac53\right],\;\left(-\frac53;\;\frac12\right],\;\left(\frac12;\;+\infty\right)](https://tex.z-dn.net/?f=%5Cleft%28-%5Cinfty%3B%5C%3B-%5Cfrac53%5Cright%5D%2C%5C%3B%5Cleft%28-%5Cfrac53%3B%5C%3B%5Cfrac12%5Cright%5D%2C%5C%3B%5Cleft%28%5Cfrac12%3B%5C%3B%2B%5Cinfty%5Cright%29 "\left(-\infty;\;-\frac53\right],\;\left(-\frac53;\;\frac12\right],\;\left(\frac12;\;+\infty\right)")
Рассмотрим неравенство на этих промежутках
0,\;2x-1<0\\3x+5-2x+1\geq3\\x\geq-3\\\\x\in\left(\frac12;\;+\infty\right)\\3x+5>0,\;2x-1>0\\3x+5+2x-1\geq3\\5x\geq-4\\x\geq-\frac15\\\\OTBET:\;x\in\left[-3;\;-\frac75\right]\cup\left[-\frac15;\;+\infty\right)" alt="x\in\left(-\infty;\;-\frac53\right]\\3x+5<0,\;2x-1<0\\-3x-5-2x+1\geq3\\-5x\geq7\\x\leq-\frac75\\\\x\in\left(-\frac53;\;\frac12\right]\\3x+5>0,\;2x-1<0\\3x+5-2x+1\geq3\\x\geq-3\\\\x\in\left(\frac12;\;+\infty\right)\\3x+5>0,\;2x-1>0\\3x+5+2x-1\geq3\\5x\geq-4\\x\geq-\frac15\\\\OTBET:\;x\in\left[-3;\;-\frac75\right]\cup\left[-\frac15;\;+\infty\right)" align="absmiddle" class="latex-formula">