Question

Choose the smallest solution to the equation if there is a solution.12x - 3| +8 = 10

Answer 1

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