# How do you solve 3-6n-4<17?

Jul 21, 2018

$n > - 3$

#### Explanation:

$3 - 6 n - 4 < 17$

Simplify the left hand side:
$- 1 - 6 n < 17$

Add $\textcolor{b l u e}{6 n}$ to both sides of the inequality:
$- 1 - 6 n \quad \textcolor{b l u e}{+ \quad 6 n} < 17 \quad \textcolor{b l u e}{+ \quad 6 n}$

#-1 < 17 + 6n

Subtract $\textcolor{b l u e}{17}$ from both sides:
$- 1 \quad \textcolor{b l u e}{- \quad 17} < 17 + 6 n \quad \textcolor{b l u e}{- \quad 17}$

$- 18 < 6 n$

Divide both sides by $\textcolor{b l u e}{6}$:
$\frac{- 18}{\textcolor{b l u e}{6}} < \frac{6 n}{\textcolor{b l u e}{6}}$

$- 3 < n$

$n > - 3$

This can be said as "$n$ is greater than $- 3$." (mathwarehouse.com)

The open circle on the $- 3$ means that $- 3$ is not a solution (but anything greater than it).

Hope this helps!

Jul 21, 2018

$n > - 3$

#### Explanation:

We can simplify left side to $- 1 - 6 n$. We now have

$- 1 - 6 n < 17$

Next, we can add $1$ to both sides to get

$- 6 n < 18$

Lastly, divide both sides by $6$ to isolate $n$. Recall that since we divided by a negative, the sign flips. We're left with

$n > - 3$

Hope this helps!