[tex]\frac{2}{3}x+4\ge \:x+1\\\\\frac{2}{3}x+4-4\ge \:x+1-4\\\\\frac{2}{3}x\ge \:x-3\\\\\frac{2}{3}x-x\ge \:x-3-x\\\\-\frac{1}{3}x\ge \:-3\\\\\left(-\frac{1}{3}x\right)\left(-1\right)\le \left(-3\right)\left(-1\right)\\\\\frac{1}{3}x\le \:3\\\\3\cdot \frac{1}{3}x\le \:3\cdot \:3\\\\x\le \:9[/tex]
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[tex]\frac{2}{3}x+4\ge \:x+1\\\\\frac{2}{3}x+4-4\ge \:x+1-4\\\\\frac{2}{3}x\ge \:x-3\\\\\frac{2}{3}x-x\ge \:x-3-x\\\\-\frac{1}{3}x\ge \:-3\\\\\left(-\frac{1}{3}x\right)\left(-1\right)\le \left(-3\right)\left(-1\right)\\\\\frac{1}{3}x\le \:3\\\\3\cdot \frac{1}{3}x\le \:3\cdot \:3\\\\x\le \:9[/tex]