1.

Solve `|x+1|gt4,x inR`.

Answer» We have,`|x|gtaiffxlt-aorxgta`.
`therefore |x+1|gt4 iffx+1lt-4orx+1gt4`
`iff xlt-4-1orxgt4-1`
`iff x lt-5orxgt3`
`iff x in(-oo,-5)orx in(3,oo)`.
`therefore` solution set `=(-oo,-5)uu(3,oo)`.


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