Answer:
[tex]\large\boxed{x<-\dfrac{117}{7}\ or\ x>\dfrac{17}{7}}\\\downarrow\\\boxed{x\in\left(-\infty,\ -\dfrac{117}{7}\right)\ \cup\ \left(\dfrac{17}{7};\ \infty\right)}[/tex]
Step-by-step explanation:
[tex]|0.7x+5|>6.7\iff0.7x+5>6.7\ or\ 0.7x+5<-6.7\\\\(1)\\0.7x+5>6.7\qquad\text{subtract 5 from both sides}\\0.7x>1.7\qquad\text{divide both sides by 0.7}\\x>\dfrac{1.7}{0.7}\to x>\dfrac{17}{7}\\\\(2)\\0.7x+5<-6.7\qquad\text{subtract 5 from both sides}\\0.7x<-11.7\qquad\text{divide both sides by 0.7}\\x<\dfrac{-11.7}{0.7}\to x<-\dfrac{117}{7}\\\\\text{From (1) and (2) we have}\\x<-\dfrac{117}{7}\ or\ x>\dfrac{17}{7}\to x\in\left(-\infty,\ -\dfrac{117}{7}\right)\ \cup\ \left(\dfrac{17}{7};\ \infty\right)[/tex]
