Question

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

Answer 1

`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

`rarrcolor(red)(6(n-2))>5n+5`

Use the distributive property to expand `6(n-2)`

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

`rarrcolor(red)(6(n)-6(2))>5n+5`

`rarr6n-12>5n+5`

Add `12` both sides

`rarr6n-12+color(red)(12)>5n+5+color(red)(12)`

`rarr6n>5n+17`

Subtract `5n` both sides

`rarr6n-color(red)(5n)>5n+17-color(red)(5n)`

`color(green)(rArrn>17`

Hopefully this helps!