# How do you solve 1/4n+12>=3/4n-4 and graph the solution on a number line?

Oct 13, 2017

$n \le 32$

#### Explanation:

$\frac{1}{4} n + 16 \le \frac{3}{4} n$
subtract $\frac{1}{4} n$ from both sides
$16 \le \frac{1}{2} n$
divide $16$ by $\frac{1}{2}$
it looks like this
$\frac{16}{1} \cdot \frac{2}{1}$
your answer is $32$
so your final equation is $n \le 32$
on a number line, put a closed circle on 32 and draw the line going towards the negatives indefinitely.

Here is the graph

Oct 13, 2017

$n \le 32$

#### Explanation:

$\frac{1}{4} n + 12 \ge \frac{3}{4} n - 4$
Let's start by subtracting $\textcolor{red}{\frac{3}{4} n}$ from both sides
$\frac{1}{4} n + 12 - \textcolor{red}{\frac{3}{4} n} \ge \cancel{\frac{3}{4} n} - 4 \cancel{\textcolor{red}{- \frac{3}{4} n}}$
$\frac{- 1}{2} n + 12 \ge - 4$
Then, we can subtract $\textcolor{g r e e n}{12}$ from both sides
$\frac{- 1}{2} n + \cancel{12} - \cancel{\textcolor{g r e e n}{12}} \ge - 4 - \textcolor{g r e e n}{12}$
$\frac{- 1}{2} n \ge - 16$
In order to find $n$, we need to multiply both sides by $\textcolor{\mathmr{and} a n \ge}{\frac{2}{- 1}}$
$\textcolor{\mathmr{and} a n \ge}{\left(\frac{2}{-} 1\right)} \left(\frac{- 1}{2} n\right) \ge \textcolor{\mathmr{and} a n \ge}{\frac{2}{-} 1} \left(- 16\right)$
$\cancel{\frac{- 2}{-} 2 n} \ge \left(\frac{- 32}{-} 1\right)$
$n \le 32$