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Answer: [tex]\begin{bmatrix}\mathrm{Solution:}\:&\:x\le \:-\frac{2}{3}\quad \mathrm{or}\quad \:x\ge \:0\:\\ \:\mathrm{Decimal:}&\:x\le \:-0.66666\dots \quad \mathrm{or}\quad \:x\ge \:0\\ \:\mathrm{Interval\:Notation:}&\:(-\infty \:,\:-\frac{2}{3}]\cup \:[0,\:\infty \:)\end{bmatrix}[/tex]
Step-by-step explanation:
[tex]\left|x-2\right|+\left|2x+1\right|\ge \:3[/tex]
[tex]x<-\frac{1}{2},\:\space-\frac{1}{2}\le \:x<2,\:\spacex\ge \:2[/tex]
[tex]x\le \:-\frac{2}{3}\quad \mathrm{or}\quad \:0\le \:x<2\quad \mathrm{or}\quad \:x\ge \:2[/tex]
[tex]x\le \:-\frac{2}{3}\quad \mathrm{or}\quad \:x\ge \:0[/tex]