1.

Solve `|3-4x|ge9, x in R`.

Answer» We have, `|x|gea iff x le-aorxgea`.
`therefore |3-4x|ge9 iff3-4x le-9or3-4x ge9`
`iff -4xle-9-3 or -4xge 9-3`
`iff -4xle-12or -4x ge6`
`iffx ge3 or le(-3)/(2)`
`iff x le(-3)/(2)orxge3`
`iff x in(-oo, (-3)/(2)]orx in[3,oo)`.
`therefore` solution set `=(-oo,(-3)/(2)]uu[3,oo)`.


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