Solve `|4-x|lt2`.

1.	Solve `\|4-x\|lt2`.
Answer» We have, `\|x\|ltaiff-altxlta`. `therefore\|4-x\|lt2` `iff-2lt4-xlt2` `iff-2lt4-xand4-xlt2` `iff -2-4-xand-xlt2-4` `iff-6lt-xand-xlt-2` `iff 6gt x andxgt2`. `iff 2ltxlt6`. `therefore` solution set `={x inR:2ltxlt6}=(2,6)`.

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