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[典例分析]例1解下列不等式:(1)-2x~2+x+1/2<0;(2)x~2<3x+4;(3)x~2>2x-3;(4)x~2>2x-1.分析首先把每个不等式化为一元二次不等式的标准形式(移项将右边化为0,同时二次项系数化为正).结合其对应的二次函数图像写出解集.
[Example Analysis] Example 1 solves the following inequalities: (1)-2x~2+x+1/2<0; (2)x~2<3x+4; (3)x~2>2x-3; ( 4) x~2>2x-1. The analysis first transforms each inequality into a standard form of a quadratic inequality of one yuan (shifting the term to 0 on the right, and the coefficient of the quadratic term to positive). Combine its corresponding quadratic The function image writes the solution set.