How do you solve #3/10 - w = 4/5 - 3/5w#?

1 Answer
Apr 4, 2016

Answer:

#w=-5/4#

Explanation:

#1#. Add #3/5w# to both sides of the equation.

#3/10-w=4/5-3/5w#

#3/10-w# #color(red)(+3/5w)=4/5-3/5w# #color(red)(+3/5w)#

#2# Rewrite #-w# on the left side of the equation with a denominator of #5#.

#3/10-1/1w+3/5w=4/5#

#3/10-(1color(blue)(xx5))/(1color(blue)(xx5))w+3/5w=4/5#

#3/10-5/5w+3/5w=4/5#

#3#. Calculate #-5/5w+3/5w#.

#3/10-(5+3)/5w=4/5#

#3/10-2/5w=4/5#

#4#. Subtract #3/10# from both sides of the equation.

#3/10# #color(red)(-3/10)-2/5w=4/5# #color(red)(-3/10)#

#5#. Rewrite #4/5# on the right side of the equation with a denominator of #10#.

#-2/5w=4/5-3/10#

#-2/5w=(4color(blue)(xx2))/(5color(blue)(xx2))-3/10#

#-2/5w=8/10-3/10#

#6#. Calculate #8/10-3/10#.

#-2/5w=(8-3)/10#

#-2/5w=5/10#

#7#. Divide both sides of the equation by #-2/5#.

#-2/5wcolor(red)(-:-2/5)=5/10color(red)(-:-2/5)#

#8#. Solve for #w#.

#w=5/10xx-5/2#

#w=5/(10color(blue)(-:5))xx-(5color(blue)(-:5))/2#

#w=5/2xx-1/2#

#color(green)(|bar(ul(color(white)(a/a)w=-5/4color(white)(a/a)|)))#