# How do you solve -4w-13> -21 and graph the solution on a number line?

Aug 3, 2017

See a solution process below:

#### Explanation:

First, add $\textcolor{red}{13}$ to each side of the inequality to isolate the $w$ term while keeping the inequality balanced:

$- 4 w - 13 + \textcolor{red}{13} > 21 + \textcolor{red}{13}$

$- 4 w - 0 > 34$

$- 4 w > 34$

Next, divide each side of the inequality by $\textcolor{b l u e}{- 4}$ to solve for $w$ while keeping the inequality balanced. However, because we are multiplying or dividing the inequality by a negative number we must reverse the inequality operator:

$\frac{- 4 w}{\textcolor{b l u e}{- 4}} \textcolor{red}{<} \frac{34}{\textcolor{b l u e}{- 4}}$

$\frac{- \textcolor{red}{\cancel{\textcolor{b l a c k}{4}}} w}{\cancel{\textcolor{b l u e}{- 4}}} \textcolor{red}{<} \frac{17 \times 2}{\textcolor{b l u e}{2 \times - 2}}$

$w \textcolor{red}{<} \frac{17 \times \textcolor{b l u e}{\cancel{\textcolor{b l a c k}{2}}}}{\textcolor{b l u e}{\textcolor{b l a c k}{\cancel{\textcolor{b l u e}{2}}} \times - 2}}$

$w < - \frac{17}{2}$

To graph this we draw a dashed vertical line at $- \frac{17}{2}$. The line is dashed to indicate the inequality is a "less than" operator and does not include the value $- \frac{17}{2}$. Then you shade to the left of the line to indicated the "less than":

graph{x < -17/2 [-15, 5, -7.5, 7.5]}