# How do you write an inequality and solve given "three times the sum of a number and seven is greater than five times the number less thirteen"?

Sep 4, 2017

$\text{see explanation}$

#### Explanation:

$\text{let n be the number}$

$\text{then the sum of this number and 7 is } n + 7$

$\text{and 3 times this sum is } 3 \left(n + 7\right)$

$\text{5 times the number less thirteen is } 5 n - 13$

$\Rightarrow 3 \left(n + 7\right) > 5 n - 13 \leftarrow \textcolor{red}{\text{ is the inequality}}$

$\text{distribute the brackets on the left side}$

$3 n + 21 > 5 n - 13$

$\text{subtract 3n from both sides}$

$\cancel{3 n} \cancel{- 3 n} + 21 > 5 n - 3 n - 13$

$\Rightarrow 21 > 2 n - 13$

$\text{add 13 to both sides}$

$21 + 13 > 2 n \cancel{- 13} \cancel{+ 13}$

$\Rightarrow 34 > 2 n$

$\text{divide both sides by 2}$

$17 > n \Rightarrow n < 17$