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

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
$\left.\left(x - 3 > 8 , \text{ AND } , x + 2 > \textcolor{b l u e}{n}\right)\right.$

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
$\left.\left(x > 11 , \text{ AND } , x > \left(\textcolor{b l u e}{n} - 2\right)\right)\right.$

Using the notation: $\max \left(a , b\right) = \left\{\begin{matrix}a \text{ if " a>=b \\ b" if } a < b\end{matrix}\right.$

Then these restrictions can be combined into the single restriction:
$x > \max \left(8 , \textcolor{b l u e}{n} - 2\right)$
or
in the requested interval notation:
$x \in \left(\max \left(8 , \textcolor{b l u e}{n} - 2\right) , + \infty\right)$