How do you solve #-3( y + 2.5) = 6.9- 4.2y#?

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Answer 1 · 2017-07-03T15:55:11

See a solution process below:

First, expand the terms on the left side of the equation by multiplying each term within the parenthesis by the term outside the parenthesis:

#color(red)(-3)(y + 2.5) = 6.9 - 4.2y#

#(color(red)(-3) xx y) + (color(red)(-3) xx 2.5) = 6.9 - 4.2y#

#-3y - 7.5 = 6.9 - 4.2y#

Next, add #color(red)(7.5)# and #color(blue)(4.2y)# to each side of the equation to isolate the #y# term while keeping the equation balanced:

#-3y - 7.5 + color(red)(7.5) + color(blue)(4.2y) = 6.9 - 4.2y + color(red)(7.5) + color(blue)(4.2y)#

#-3y + color(blue)(4.2y) - 7.5 + color(red)(7.5) = 6.9 + color(red)(7.5) - 4.2y + color(blue)(4.2y)#

#(-3 + color(blue)(4.2))y - 0 = 14.4 - 0#

#1.2y = 14.4#

Now, divide each side of the equation by #color(red)(1.2)# to solve for #y# while keeping the equation balanced:

#(1.2y)/color(red)(1.2) = 14.4/color(red)(1.2)#

#(color(red)(cancel(color(black)(1.2)))y)/cancel(color(red)(1.2)) = 12#

#y = 12#