91影视

For real numbers $a\text{and}b$with b>0

Absolute value inequality is $\left|a\right|<b$ when $-b<a\text{and}a<b$, and

Absolute value inequality is $\left|a\right|>b$ when $a<-b\text{or}a>b$

Properties of inequalities are written in following table:

From definition of absolute value inequality, given expression is simplified to

$-n<n-3\text{and}n-3<n$

Use subtraction and division property of inequality, subtract with same number does not change the sign of inequality. Also division by same positive number does not reverse the sign of inequality as shown below

$\begin{array}{c}鈭�n鈭�n<n鈭�n鈭�3\text{and}n鈭�n鈭�3<n鈭�n\\ 鈭�2n<鈭�3\text{and}鈭�3<0\\ \frac{鈭�2n}{鈭�2}>\frac{鈭�3}{鈭�2}\text{and}鈭�3<0\\ n>\frac{3}{2}\text{and}鈭�3<0\left(\text{True}\right)\end{array}$

Solution is 鈥淩eal number greater than $\frac{3}{2}$鈥� and 鈥淎ll real number鈥�

The solution of compound inequality containing and is the intersection of the solution set of the two inequalities.

So solution is real number greater than $\frac{3}{2}$

Solution is all real number greater than $\frac{3}{2}$ so number line starts from $\frac{3}{2}$ to $鈭�$

Open circle on $\frac{3}{2}$ shows this points is not included in the solution.