# How do you define a variable and write an expression for each phrase: 6 times a number increased by 3?

Sep 2, 2016

Without a comma it is difficult to know what is meant.

$\textcolor{red}{\text{6 times a number}} ,$ increased by 3 $\rightarrow \textcolor{red}{6 x} + 3$

6 times, $\textcolor{b l u e}{\text{a number increased by 3}} \rightarrow \textcolor{b l u e}{6} \left(x + 3\right)$

#### Explanation:

People often ask if punctuation is important. The importance of clearly written phrases cannot be stressed enough!
The use of a comma helps to indicate exactly what is meant.
There is no comma shown, so what is intended is not totally clear.

This expression can be read in two ways:
Note the position of the comma in each case.

Let the number be $x \text{ " larr}$ always define the variable.

$\textcolor{red}{\text{6 times a number}} ,$ increased by 3"

"Times" means multiply and "increased by 3" means 3 is added.

$\textcolor{red}{6 x} + 3$

OR

"6 times, $\textcolor{b l u e}{\text{a number increased by 3}}$

$6 \textcolor{b l u e}{\left(x + 3\right)}$