# Seven less than the product of twice a number is greater than 5 more an the same number. Which integer satisfies this inequality?

Jan 5, 2017

Any integer $13$ or greater

#### Explanation:

Translating into an algebraic form (using $n$ as the number):
Seven less than the product of twice a number is greater than 5 more than the same number.

$\rightarrow$Seven less than $\left(2 \times n\right)$ is greater than $5 + n$

$\rightarrow \left(2 n\right) - 7$ is greater than $5 + n$

$\rightarrow 2 n - 7 > 5 + n$

Subtracting $n$ from both sides
then adding $7$ to both sides
(note, you can add or subtract any amount to both sides of an inequality while maintaining the inequality)
gives:
$\textcolor{w h i t e}{\text{XXX}} n > 12$

So any integer number $13$ or greater would satisfy the given requirement.