Question

How do you solve and write the following in interval notation: `|x-1|-4>=5`?

Answer 1

`x in {(-oo,8],[10,+oo)}`

Explanation:

`abs(x-1)-4 >= 5`

`rArr abs(x-1) >= 9`

This breaks down into 2 cases:
#{: ("if "x < 1,color(white)("XXXXXXXX"),"if " x >=1), (color(white)("XX")1-x >=9,,color(white)("XX")x-1 >= 9), (color(white)("XX")-x >= 8,,color(white)("XX")x>=10), (color(white)("XX")x <= -8,,) :}#

So we have
`color(white)("XX")`either `x <= -8`
`color(white)("XX")`or `color(white)("XX")x >=10`