How do you solve #-\frac { 2} { u - 7} = - 8#?

2 Answers
Apr 19, 2017

See the entire solution process below: #u = 29/4#

Explanation:

First, multiply each side of the equation by #color(red)(u - 7)# to eliminate the fraction while keeping the equation balanced:

#color(red)(u - 7) * -2/(u - 7) = -8 * (color(red)(u - 7))#

#cancel(color(red)(u - 7)) * -2/color(red)(cancel(color(black)(u - 7))) = (-8 * color(red)(u)) + (-8 * color(red)(-7))#

#-2 = -8u + 56#

Next, subtract #color(red)(56)# from each side of the equation to isolate the #u# term while keeping the equation balanced:

#-2 - color(red)(56) = -8u + 56 - color(red)(56)#

#-58 = -8u + 0#

#-58 = -8u#

Now, divide each side of the equation by #color(red)(-8)# to solve for #u# while keeping the equation balanced:

#(-58)/color(red)(-8) = (-8u)/color(red)(-8)#

#(-2 * 29)/color(red)(-2 * 4) = (color(red)(cancel(color(black)(-8)))u)/cancel(color(red)(-8))#

#(color(red)(cancel(color(black)(-2))) * 29)/color(red)(color(black)(cancel(color(red)(-2))) * 4) = u#

#29/4 = u#

#u = 29/4#

Apr 19, 2017

#u=29/4#

Explanation:

#-2/(u-7)=-8#

Divide both sides by #-1#.

#2/(u-7)=8#

Multiply both sides by #(u - 7)# in order to get the variable out of the denominator.

#2=8(u-7)#

Then divide both sides by #8# in order to isolate #(u - 7)#.

#2/8=u-7#

Then add 7 to both sides to isolate #u#.

#7+2/8=u#

Then simplify to get:

#u=7+1/4=28/4+1/4=29/4#