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#