# How do you solve -5 > -5-3w?

Sep 1, 2015

$w > 0$

#### Explanation:

Right from the start, you can say that you need $w$ to be positive because any negative value of $w$ would make the product $\left(- 3 \cdot w\right)$ positive, which in turn will make the right-hand side of the inequality bigger than $\left(- 5\right)$.

SInce you need the left-hand side of the inequality to be strictly greater than the right-hand side, you cannot have $w = 0$, since that would imply that

$- 5 > - 5 - 3 \cdot 0$

$- 5 \textcolor{red}{\cancel{\textcolor{b l a c k}{>}}} - 5$

So, the solution set for this inequality is $w > 0$.

$- 5 > - 5 - 3 w$

$- \textcolor{red}{\cancel{\textcolor{b l a c k}{5}}} + \textcolor{red}{\cancel{\textcolor{b l a c k}{5}}} > - 3 w$

$0 > - 3 w \implies w > 0$