91Ó°ÊÓ

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

$$" width="9" height="19" role="math">−5≤3w+2and3w+2≤5

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

$\begin{array}{c}−5−2≤3w+2−2\text{and}3w+2−2≤5−2\\ −7≤3w\text{and}3w≤3\\ −\frac{7}{3}≤\frac{3w}{3}\text{and}\frac{3w}{3}≤\frac{3}{3}\\ −\frac{7}{3}≤w\text{and}w≤1\end{array}$

For $-\frac{7}{3}≤w\text{and}w≤1$, number line starts from $-\frac{7}{3}$ to 1

Dot on $-\frac{7}{3}\text{and 1}$ shows these points are included in the solution.