# How do you solve \frac { 3} { w - 6} = - 4?

May 23, 2017

See a solution process below:

#### Explanation:

First, multiply each side of the equation by $\frac{\textcolor{red}{\left(w - 6\right)}}{\textcolor{b l u e}{- 4}}$ to isolate the expression with $w$ on the right side of the equation while keeping the equation balanced:

$\frac{\textcolor{red}{\left(w - 6\right)}}{\textcolor{b l u e}{- 4}} \times \frac{3}{w - 6} = \frac{\textcolor{red}{\left(w - 6\right)}}{\textcolor{b l u e}{- 4}} \times - 4$

$\frac{\cancel{\textcolor{red}{\left(w - 6\right)}}}{\textcolor{b l u e}{- 4}} \times \frac{3}{\textcolor{red}{\cancel{\textcolor{b l a c k}{w - 6}}}} = \frac{\textcolor{red}{\left(w - 6\right)}}{\cancel{\textcolor{b l u e}{- 4}}} \times \textcolor{b l u e}{\cancel{\textcolor{b l a c k}{- 4}}}$

$- \frac{3}{4} = w - 6$

Now, add $\textcolor{red}{6}$ to each side of the equation to solve for $w$ while keeping the equation balanced:

$- \frac{3}{4} + \textcolor{red}{6} = w - 6 + \textcolor{red}{6}$

$- \frac{3}{4} + \left(\frac{4}{4} \times \textcolor{red}{6}\right) = w - 0$

$- \frac{3}{4} + \frac{24}{4} = w$

$\frac{21}{4} = w$

$w = \frac{21}{4}$

May 23, 2017

Answer: $\frac{21}{4}$ . See below for steps! : )

#### Explanation:

$\frac{3}{w} - 6 = - 4$

Step 1: Multiply both sides by w-6.
3=−4w+24

−4w+24=3(Flip the equation)

−4w+24−24=3−24(Subtract 24 from both sides)

−4w=−21

w=$\frac{21}{4}$

Check answers. (Plug them in to make sure they work.)

$\frac{21}{4}$ (Works in original equation)

Answer: $\frac{21}{4}$

I hope it helps you!

May 23, 2017

$w = \frac{21}{4}$

#### Explanation:

Given:$\text{ } \frac{3}{w - 6} = - 4$

We need to have the $w$ in the numerator (top of the fraction). So turn both sides upside down.

$\frac{w - 6}{3} = - \frac{1}{4}$

Multiply both sides by 3

$w - 6 = - \frac{3}{4}$

$w = \frac{21}{4}$