Question

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

Answer 1

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 `2n`

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:

`2n > n + 9`

To solve, subtract `color(red)(n)` from each side of the inequality to find `n` while keeping the inequality balanced:

`2n - color(red)(n) > n - color(red)(n) + 9`

`2n - 1color(red)(n) > 0 + 9`

`(2 - 1)n > 9`

`1n > 9`

`n > 9`