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## Homework Statement

[tex]|2x-1|+|x+2|\geq 4x[/tex]

## Homework Equations

## The Attempt at a Solution

For x<-2 , [tex]-(2x-1)-(x+2)\geq 4x[/tex]

[tex]x\leq -\frac{1}{7}[/tex]

For [tex]x\geq \frac{1}{2}[/tex]

[tex]2x-1+x+2\geq 4x[/tex]

[tex]x\leq 1[/tex]

For [tex]-2 \leq x < \frac{1}{2}[/tex] ,

[tex]-(2x-1)+x+2\geq 4x [/tex]

[tex]x\leq \frac{3}{5}[/tex]

after combining , the solution would be [tex]x\leq -\frac{1}{7} [/tex]

AM i correct ? but the answer given is [tex]x\leq 1[/tex]