Question

解不等式.

Answer 1

解:不等式中x的取值范围是x≠0,x≠1.

(1)当x＜0时,x-1＜0,|x|=-x＞0,

∴原不等式变形为-2x²＜x-1,

解得x＜-1或x＞,又由x＜0,求交集后得x＜-1.

(2)当0＜x＜1时,x-1＜0,|x|=x＞0,

∴原不等式变形为2x²＜x-1,解之,得解集为.

(3)当x＞1时,x-1＞0,|x|=x＞0,

∴原不等式变形为2x²＞x-1,解集为R,与x＞1求交集后为x＞1.

综上,可得原不等式的解集为{x|x＜-1或x＞1}.