# How do you write an inequality and solve given "twice a number is more than the sum of that number and 9"?

Mar 12, 2017

See the entire solution process below

#### Explanation:

First, let's call the number we are looking for $n$.

Now, we can write "twice a number" as $2 n$

And, we can write "the sum of that number and 9" as $n + 9$

The first "is more than" so we can write the inequality as:

$2 n > n + 9$

To solve, subtract $\textcolor{red}{n}$ from each side of the inequality to find $n$ while keeping the inequality balanced:

$2 n - \textcolor{red}{n} > n - \textcolor{red}{n} + 9$

$2 n - 1 \textcolor{red}{n} > 0 + 9$

$\left(2 - 1\right) n > 9$

$1 n > 9$

$n > 9$