Question

How do you solve `abs(x-20<4`?

Answer 1

Alternative Version of Question 1
`abs(x) - 20 <4`
`color(white)("XXXXX")` `abs(x) < 24`
`color(white)("XXXXX")` `rarr -24 < x < 24`

Alternate Version of Question 2
`abs(x-20) <4`
`color(white)("XXXXX")`Case 1: `(x-20)<0 rarr x < 20`
`color(white)("XXXXX")` `color(white)("XXXXX")` `abs(x-20) < 4`
`color(white)("XXXXX")` `color(white)("XXXXX")` `20-x < 4`
`color(white)("XXXXX")` `color(white)("XXXXX")` `x > 16`
`color(white)("XXXXX")` `16 < x < 20`

`color(white)("XXXXX")`Case2: `(x-20)>=0 rarr x>= 20`
`color(white)("XXXXX")` `color(white)("XXXXX")` `abs(x-20) < 4`
`color(white)("XXXXX")` `color(white)("XXXXX")` `x-20 < 4`
`color(white)("XXXXX")` `color(white)("XXXXX")` `x < 24`
`color(white)("XXXXX")` `20 <= x < 24`

Combining Case 1 and Case 2
`color(white)("XXXXX")` `16 < x < 24`