Question

How do you write each specification as an absolute value inequality: 6.3 (is less than or equal to) h (is less than or equal to) 10.3?

Answer 1

`abs(h-8.3) <= 2`

Explanation:

Given `6.3 <= h <= 10.3`

The midpoint between `6.3` and `10.3` is `8.3`

Remember that we can subtract the same amount for both sides of an inequality and still maintain the validity of the inequality:

`color(white)("XXX")6.3-8.3 <= h-8.3 <= 10.3 - 8.3`

`color(white)("XXX")-2 <= h-8.3 <= 2`

which we could split up as
`color(white)("XXX")-2 <= h-8.3 color(white)("X")rarrcolor(white)("X")-(h-8.3) <= 2`
and
`color(white)("XXX")h-8.3 <= 2`

which recombines as
`color(white)("XXX")abs(h-8.3) <=2`