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

1 Answer
Jan 13, 2018

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)