[tex]\begin{gathered} -3+4|2x-5|=14 \\ -3+4\mleft|2x-5\mright|+3=14+3 \\ 4\mleft|2x-5\mright|=17 \\ \frac{4\left|2x-5\right|}{4}=\frac{17}{4} \\ \mleft|2x-5\mright|=\frac{17}{4} \\ 2x-5=-\frac{17}{4}\quad \mathrm{or}\quad \: 2x-5=\frac{17}{4} \end{gathered}[/tex]
then
[tex]\begin{gathered} 2x-5=\frac{17}{4} \\ 2x-5+5=\frac{17}{4}+5 \\ 2x=\frac{37}{2} \\ \frac{2x}{2}=\frac{37}{2}\frac{\cdot}{\cdot}2 \\ x=\frac{37}{4} \end{gathered}[/tex]
answer: x = 37/4 and x = 3/8
