How do you solve #5.3 + u = 3.2u -2.7#?

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Answer 1 · 2016-06-04T17:54:00

#color(blue)(u = 3.64#

#5.3 + u = 3.2 u − 2.7 #

#5.3 + color(blue)(u) = color(blue)(3.2 u) − 2.7 #

#5.3 + 2.7 = color(blue)(3.2 u − u ) #

#8 = 2.2u #

#u = 8/(2.2) #

#color(blue)(u = 3.64# rounded to the nearest #100#

Answer 2 · 2016-06-04T19:53:53

Same thing with a touch more explanation

# u= 3 11/23 " this is an exact answer!"#

Given:#" "color(brown)(5.3+u=3.2u-2.7)#

Subtract #color(blue)(u)# from both sides

#" "color(brown)(5.3+ucolor(blue)(-u)=3.2u-2.7color(blue)(-u))#

But #u-u=0#

#" "5.3+0=3.2u-u-2.7#

But #3.2u-u=2.3u#

#" "5.3=2.3u-2.7#

Add #color(blue)(2.7)# to both sides

#" "color(brown)(5.3color(blue)(+2.7)=2.3u-2.7color(blue)(+2.7)#

But #5.3+2.7 = 8.0" and "-2.7+2.7=0#

#" "8=2.3u+0#

Divide both sides by 2.3

#" "8/2.3=2.3/2.3xxu#

But #2.3/2.3=1" so "u=8/2.3#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

But dividing #2.3" into "8# gives a never ending decimal so the answer would not be accurate. It is much more accurate to express it as a fraction.

So write #" "u=8/2.3" "# as #" "u=(8xx10)/(2.3xx10)= 80/23#

#=> u= 3 11/23#