[tex]\begin{gathered} |\frac{1}{4}x-3|+8\text{ =10 is} \\ |\frac{1}{4}x-3|=2 \\ \text{this means that} \\ \frac{1}{4}x-3\text{ = 2 if }\frac{1}{4}x-3\text{ >0 or} \\ \frac{1}{4}x-3\text{ =- 2 if }\frac{1}{4}x-3\text{ <0 .} \\ \text{First posibility: }\frac{1}{4}x-3\text{ >0. then:} \\ \frac{1}{4}x-3\text{ = 2 and you have} \\ \frac{1}{4}x\text{ =}5\text{ and finally: x=20} \\ In\text{ the last posibility, }\frac{1}{4}x-3<0\text{ , then} \\ \frac{1}{4}x-3\text{ =- 2 or} \\ \frac{1}{4}x=1,\text{ and finally} \\ x=4 \\ 4|x-8|\text{ +8 <4 then} \\ 4|x-8|<-4\text{ or} \\ |x-8|<-1 \end{gathered}[/tex]
