We are asked to solve for x.
[tex]2|\frac{x}{3}|<-10[/tex]
Solution
[tex]\begin{gathered} 2|\frac{x}{3}|<-10 \\ \text{Divide both sides by 2} \\ |\frac{x}{3}|<-\frac{10}{2} \\ |\frac{x}{3}|<-5 \\ \\ |x|\times\frac{1}{|3|}<-5 \\ \\ \frac{|x|}{3}<-5 \\ \text{Multiply both sides by 3} \\ |x|<-5\times3 \\ |x|<-15 \\ x\text{ can either be positive or negative.} \\ \\ \text{If x is positive:} \\ x<-15 \\ \\ \text{If x is negative:} \\ -x<-15 \\ \text{Divide both sides by -1} \\ x>15 \end{gathered}[/tex]
Answer
Thus, the answer is :
[tex]x<-15\text{ or }x>15[/tex]
