(a) 画出 $y=|2x+3|$ 的图像草图。

(b) 解不等式 $3x+8>|2x+3|$。

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。

将直线 $y=2x+3$ 在横轴下方的部分向上反射，得到 V 形图。

The graph consists of the two rays

The vertex is $(-3/2,0)$ and the $y$-intercept is $(0,3)$. The branches have gradients $-2$ and $2$.

绝对值小于某个数等价于该数同时大于绝对值内表达式及其相反数。这种写法自动排除右侧为负的错误范围。

For $3x+8>|2x+3|$, both

must hold. These give

Taking the intersection,

平方前必须先要求 $3x+8>0$。平方后的二次不等式会产生额外的负区间，需与该符号条件相交。

Since $|2x+3|\ge0$, the inequality requires

Under this condition, squaring is equivalent:

Thus $x<-5$ or $x>-11/5$. Intersecting with $x>-8/3$ leaves