Question

How do you solve and write the following in interval notation: `|1 + 5x| > 11`?

Answer 1

`(-oo,-12/5)uu(2,+oo)`

Explanation:

To solve inequalities of this type, we have to solve 2 inequalities.

`|x|>a" then " x< color(red)(-a)" or " x > color(red)(a)`

`rArr1+5x< color(red)(-11)" or " 1+5x > color(red)(11)`

`color(blue)"solve " 1+5x<-11`

subtract 1 from both sides.

`cancel(1)cancel(-1)+5x< -11-1`

`rArr5x<-12`

divide both sides by 5

`(cancel(5) x)/cancel(5)<(-12)/5`

`rArrx<-12/5larrcolor(red)"first solution"`

`color(blue)"solve " 1+5x>11`

`rArr5x>10`

`rArrx>2larrcolor(red)" second solution"`

`"Expressing the solution in interval notation"`

`(-oo,-12/5)uu (2,+oo)`