Question

12x+7<-11 or 5x-8>40

Answer 1

`\large\boxed{x<-1(1)/(2)\ or\ x>9(3)/(5)\to x\in\left(-\infty,\ -1(1)/(2)\right)\ \cup\ \left(9(3)/(5),\ \infty\right)}`

Explanation:

`12x+7<-11\qquad\text{subtrct 7 from both sides}\\\\12x+7-7<-11-7\\\\12x<-18\qquad\text{divide both sides by 12}\\\\(12x)/(12)<(-18)/(12)\\\\x<-(18:6)/(12:6)\\\\x<-(3)/(2)\\\\x<-1(1)/(2)\\===========================`

`5x-8>40\qquad\text{add 8 to both sides}\\\\5x-8+8>40+8\\\\5x>48\qquad\text{divide both sides by 5}\\\\(5x)/(5)>(48)/(5)\\\\x>(48)/(5)\\\\x>9(3)/(5)\\===========================`

`x<-1(1)/(2)\ or\ x>9(3)/(5)`