Question

What is the solution of 5 - 2x > -3 or -3x + 9 < -6?

Answer 1

`\large\boxed{x<4\ or\ x>5\to x\in(-\infty,\ 4)\ \cup\ (5,\ \infty)}`

Explanation:

`(1)\\5-2x>-3\ or\ -3x+9<-6\\\\5-2x>-3\qquad\text{subtract 5 from both sides}\\\\-2x>-8\qquad\text{change the signs}\\\\2x<8\qquad\text{divide both sides by 2}\\\\x<4`

`(2)\\-3x+9<-6\qquad\text{subtract 9 from both sides}\\\\-3x<-15\qquad\text{change the signs}\\\\3x>15\qquad\text{divide both sides by 3}\\\\x>5`

`\text{From (1) and (2) we have}\ x<4\ or\ x>5\to x\in(-\infty,\ 4)\ \cup\ (5,\ \infty)`