Given the definition of absolute value:
[tex]\begin{gathered} |a|=\begin{cases}a,a\ge0 \\ -a,a<0\end{cases} \\ \end{gathered}[/tex]in this case we have the following:
[tex]|5-2x|-11=0[/tex]we will have two cases from this equation.
The first case is when 5-2x>=0, then we have the following:
[tex]\begin{gathered} 5-2x-11=0 \\ \Rightarrow-2x-6=0 \\ \Rightarrow-2x=6 \\ \Rightarrow x=\frac{6}{-2}=-3 \\ x=-3 \end{gathered}[/tex]next, we will consider the cas when 5-2x < 0, then we would have the following:
[tex]\begin{gathered} -(5-2x)-11=0 \\ \Rightarrow-5+2x-11=0 \\ \Rightarrow2x-16=0 \\ \Rightarrow2x=16 \\ \Rightarrow x=\frac{16}{2}=8 \\ x=8 \end{gathered}[/tex]therefore, the two x-values that are solutions to the equation are x=-3 and x=8
