# Question 9c6b8

Dec 8, 2016

Not sure what you are asking!

$n < 1.6$

#### Explanation:

Assumption:

The question is asking for the value of $n$ to be determined given that:

$\text{ } \textcolor{b r o w n}{8 n - 10 < 6 - 2 n}$

$\textcolor{g r e e n}{\text{Treat this as if it were: } 8 n - 10 = 6 - 2 n}$

$\textcolor{g r e e n}{\text{In inequalities you have to turn the inequality sign round the other way}}$
$\textcolor{g r e e n}{\text{if you multiply by -1. It is NOT THE CASE in this question.}}$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Add $\textcolor{b l u e}{2 n}$ to both sides

$\text{ } \textcolor{b r o w n}{8 n \textcolor{b l u e}{+ 2 n} - 10 < 6 - 2 n \textcolor{b l u e}{+ 2 n}}$

But $- 2 n + 2 n = 0$ giving:

$\text{ } \textcolor{b r o w n}{10 n - 10 < 6}$

Add $\textcolor{b l u e}{10}$ to both sides

$\text{ } \textcolor{b r o w n}{10 n \textcolor{b l u e}{+ 10} - 10 < 6 \textcolor{b l u e}{+ 10}}$

$\text{ } \textcolor{b r o w n}{10 n < 16}$

Divide both sides by 10

" "color(brown)(10/(color(blue)(10))n<16/(color(blue)(10))#

But $\frac{10}{10} = 1$

$\text{ } \textcolor{b r o w n}{n < 1.6}$