Question

|0.7x+5|>6.7

Help plz

Answer 1

`\large\boxed{x<-(117)/(7)\ or\ x>(17)/(7)}\\\downarrow\\\boxed{x\in\left(-\infty,\ -(117)/(7)\right)\ \cup\ \left((17)/(7);\ \infty\right)}`

Explanation:

`|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>(1.7)/(0.7)\to x>(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<(-11.7)/(0.7)\to x<-(117)/(7)\\\\\text{From (1) and (2) we have}\\x<-(117)/(7)\ or\ x>(17)/(7)\to x\in\left(-\infty,\ -(117)/(7)\right)\ \cup\ \left((17)/(7);\ \infty\right)`