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

First, multiply each side of the equation by `color(red)((w - 6))/color(blue)(-4)` to isolate the expression with `w` on the right side of the equation while keeping the equation balanced:

`color(red)((w - 6))/color(blue)(-4) xx 3/(w - 6) = color(red)((w - 6))/color(blue)(-4) xx -4`

`cancel(color(red)((w - 6)))/color(blue)(-4) xx 3/color(red)(cancel(color(black)(w - 6))) = color(red)((w - 6))/cancel(color(blue)(-4)) xx color(blue)(cancel(color(black)(-4)))`

`-3/4 = w - 6`

Now, add `color(red)(6)` to each side of the equation to solve for `w` while keeping the equation balanced:

`-3/4 + color(red)(6) = w - 6 + color(red)(6)`

`-3/4 + (4/4 xx color(red)(6)) = w - 0`

`-3/4 + 24/4 = w`

`21/4 = w`

`w = 21/4`

Let's solve your equation step-by-step.
`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=`21/4`

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

`21/4` (Works in original equation)

Answer: `21/4`

I hope it helps you!

Given:`" "3/(w-6)=-4`

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

`(w-6)/3=-1/4`

Multiply both sides by 3

`w-6=-3/4`

Add 6 to both sides

`w=21/4`