解不等式 $3|x+4|>|2x-1|$。

Answer all questions. You should use a calculator where appropriate.

You must show all necessary working clearly; no marks will be given for unsupported answers from a calculator.

Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question.

请回答所有题目。适当时应使用计算器。必须清楚展示所有必要的计算过程；仅给出计算器答案而没有过程，不予评分。除非题目另有精度要求，非精确数值答案保留 3 位有效数字，以度为单位的角度保留 1 位小数。

两边都是非负量，可以等价地平方。把平方差分解，再根据两个一次因子的符号判断。

Squaring is equivalent because both sides are nonnegative. Thus

is equivalent to

or $(x+13)(5x+11)>0$. The two factors have the same sign outside their roots, giving $x<-13$ or $x>-11/5$.

也可以先根据 $x+4$ 的符号去掉左边绝对值。对正数 $c$，$|b|<c$ 等价于 $-c<b<c$。

For $x<-4$, the inequality becomes $|2x-1|<-3x-12$. This requires both

giving $x<-11/5$ and $x<-13$, hence $x<-13$.

At $x=-4$, the left side is zero and the inequality fails. For $x>-4$, it becomes $|2x-1|<3x+12$, requiring $x>-13$ and $x>-11/5$. Thus $x>-11/5$. Combining gives $x<-13$ or $x>-11/5$.