Given the absolute inequality
[tex]2|x+3|+1>3[/tex]
The absolute in equality can be written as:
[tex]\begin{gathered} 2|x+3|+1>3 \\ 2|x+3|>3-1 \\ |x+3|>\frac{2}{2} \\ |x+3|>1 \end{gathered}[/tex]
Sloving the inequality above, we can split it into two, then we will have;
[tex]\begin{gathered} -1>|x+3|\text{and }|x+3|>1 \\ \end{gathered}[/tex]
Solving the left hand side equation
[tex]\begin{gathered} |x+3|<-1 \\ x<-3-1 \\ x<-4 \end{gathered}[/tex]
To solve for the right hand side we have
[tex]\begin{gathered} |x+3|>1 \\ x+3>1 \\ x>1-3 \\ x>-2 \end{gathered}[/tex]
The graph of the inequality on the number line is shown below
Hence the solution of the inequality is x< -4 and x> -2
