How do you solve #-4( - \frac{7}{3} v + \frac{5}{2} ) = - \frac{398}{9}#?

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Answer 1 · 2016-09-20T10:48:51

#v = -3 2/3#

#-4( - \frac{7}{3} v + \frac{5}{2} ) = - \frac{398}{9}#

Instead of multiplying the (-4) into the bracket, divide both sides by (-4) first. This removes the brackets and makes the numbers smaller.

#(-4)/(color(blue)(-4))( - \frac{7}{3} v + \frac{5}{2} ) = \frac{-398}{9 (color(blue)(-4))}#

# - \frac{7}{3} v + \frac{5}{2} = 99.5/9#

Get rid of the denominators by multiplying by the LCD which is 18.

#-(color(red)(cancel18^6)xx7)/cancel3v +(color(red)(cancel18^9)xx5)/cancel2 = (color(red)(cancel18^2)xx99.5)/cancel9#

#-42v +45 = 199#

#-42v = 199-45#

#-42v = 154" "larr div -42#

#v = -3 2/3#