Question

|x-2| + |2x+1| ≥ 3
How to solve this inequality? HELP

Answer 1

Answer:
`\begin{bmatrix}\mathrm{Solution:}\:&\:x\le \:-(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 \:,\:-(2)/(3)]\cup \:[0,\:\infty \:)\end{bmatrix}`

Explanation:

`\left|x-2\right|+\left|2x+1\right|\ge \:3`

`x<-(1)/(2),\:\space-(1)/(2)\le \:x<2,\:\spacex\ge \:2`

`x\le \:-(2)/(3)\quad \mathrm{or}\quad \:0\le \:x<2\quad \mathrm{or}\quad \:x\ge \:2`

`x\le \:-(2)/(3)\quad \mathrm{or}\quad \:x\ge \:0`