The given equation is
[tex]|2x+3|+4=1[/tex]First, we need to isolate the absolute value, we'll subtract 4 one each side
[tex]\begin{gathered} |2x+3|+4-4=1-4 \\ |2x+3|=-3 \end{gathered}[/tex]Now, we rewrite the equation in two equations
[tex]\begin{gathered} 2x+3=-3 \\ 2x+3=-(-3)\rightarrow2x+3=3 \end{gathered}[/tex]Let's solve each equation
[tex]\begin{gathered} 2x+3=-3 \\ 2x=-3-3 \\ 2x=-6 \\ x=-\frac{6}{2}=-3 \end{gathered}[/tex]So, the first solution is -3.
[tex]\begin{gathered} 2x+3=3 \\ 2x=3-3=0 \\ x=\frac{0}{2}=0 \end{gathered}[/tex]The second solution is zero.
