(a) 画出 $y=|2x+1|$ 的图像草图。

(b) 解不等式 $3x+5<|2x+1|$。

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。

绝对值把直线在横轴下方的部分向上反射，顶点由 $2x+1=0$ 确定。

The graph is V-shaped:

Its vertex is $(-1/2,0)$, its $y$-intercept is $(0,1)$, and its branches have gradients $-2$ and $2$.

按 $2x+1$ 的正负分段，每段解出不等式后，还要检查是否满足分段范围。

If $x<-1/2$, then $|2x+1|=-2x-1$, so

This lies in the case $x<-1/2$.

If $x\ge-1/2$, then $|2x+1|=2x+1$, so

This is incompatible with $x\ge-1/2$.

Therefore $\boxed{x<-6/5}$.

若 $3x+5$ 为负，不等式自动成立；其余部分可以平方。这样不会因盲目平方而遗漏负数范围。

For $x<-5/3$, $3x+5<0\le|2x+1|$, so the inequality holds.

For $x\ge-5/3$, both sides are non-negative, so

Hence

This gives $-4<x<-6/5$. Intersecting with $x\ge-5/3$ gives $-5/3\le x<-6/5$.

Combining the two cases, $\boxed{x<-6/5}$.