How do you solve #\frac { 7} { 4} w - \frac { 7} { 3} = - \frac { 3} { 2} w - 3#?

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Answer 1 · 2018-01-15T15:29:58

See a solution process below: #w = -8/39#

First, add #color(red)(7/3)# and #color(blue)(3/2w)# to each side of the equation to isolate the #w# term while keeping the equation balanced:

#7/4w + color(blue)(3/2w) - 7/3 + color(red)(7/3) = -3/2w + color(blue)(3/2w) - 3 + color(red)(7/3)#

#7/4w + color(blue)(3/2w) - 0 = 0 - 3 + color(red)(7/3)#

#7/4w + color(blue)(3/2w) = -3 + color(red)(7/3)#

#7/4w + (2/2 xx color(blue)(3/2w)) = (3/3 xx -3) + color(red)(7/3)#

#7/4w + 6/4w = -9/3 + color(red)(7/3)#

#13/4w = -2/3#

Now, multiply each side of the equation by #color(red)(4)/color(blue)(13)# to solve for #w# while keeping the equation balanced:

#color(red)(4)/color(blue)(13) xx 13/4w = color(red)(4)/color(blue)(13) xx -2/3#

#cancel(color(red)(4))/cancel(color(blue)(13)) xx color(blue)(cancel(color(black)(13)))/color(red)(cancel(color(black)(4)))w = -8/39#

#w = -8/39#