# What is the solution: 6(n -2)>5n+ 5?

Oct 31, 2016

$n > 17$

#### Explanation:

color(blue)(6(n-2)>5n+5

We can solve this inequality by isolating $n$ as much as possible

We do the same operation on both sides to achieve this

$\rightarrow \textcolor{red}{6 \left(n - 2\right)} > 5 n + 5$

Use the distributive property to expand $6 \left(n - 2\right)$

color(brown)(a(b+c)=ab+ac

$\rightarrow \textcolor{red}{6 \left(n\right) - 6 \left(2\right)} > 5 n + 5$

$\rightarrow 6 n - 12 > 5 n + 5$

Add $12$ both sides

$\rightarrow 6 n - 12 + \textcolor{red}{12} > 5 n + 5 + \textcolor{red}{12}$

$\rightarrow 6 n > 5 n + 17$

Subtract $5 n$ both sides

$\rightarrow 6 n - \textcolor{red}{5 n} > 5 n + 17 - \textcolor{red}{5 n}$

color(green)(rArrn>17

Hopefully this helps!