# How do you define a variable and write an expression for each phrase: a number increased by the difference between six and a number?

Feb 26, 2016

Depending upon the interpretation, I'm going to suggest
$\textcolor{w h i t e}{\text{XXX}} n + \left\mid n - 6 \right\mid$
(see below for other possibilities)

#### Explanation:

Given the phrase:
$\textcolor{w h i t e}{\text{XXX}}$"a $\textcolor{red}{\text{number}}$ increased by the difference between six and a $\textcolor{b l u e}{\text{number}}$"
It is unclear if the intent is that both references are to the same "number". So maybe one should be a variable $n$ and the other a different variable $m$.

$\textcolor{w h i t e}{\text{XXX}}$"$\textcolor{g r e e n}{\text{...the difference between six and a number}}$"
might mean "six minus the number"
or it might mean "the absolute difference between six and the number"

With those interpretations in mind, the following are all possible intended expressions:

$n + \left(6 - n\right)$ (which would just be $6$);

$n + \left(6 - m\right)$ (two different "numbers");

$n + \left\mid 6 - n \right\mid$ (this is the one I used in the "Answer")

n+(abs(6-m) (absolute difference but two different "numbers")