Question

How do you solve and write the following in interval notation: `x − 3>8` AND `x + 2 >`?

Answer 1

Question is missing a value; see below for an approach using a variable in place of the missing value.

Explanation:

Suppose the intended restrictions were
`{:(x-3 > 8," AND ",x+2 > color(blue)n):}`

Since you can add or subtract the same amount to both sides of an inequality without changing the validity or direction of the inequality,
these are equivalent to
`{:(x > 11," AND ",x > (color(blue)n-2)):}`

Using the notation: `max(a,b)={(a" if " a>=b),(b" if " a < b):}`

Then these restrictions can be combined into the single restriction:
`x > max(8,color(blue)n-2)`
or
in the requested interval notation:
`x in (max(8,color(blue)n-2),+oo)`