How do you solve #4(x + 0.5) = 2(x - 1.5) #?

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Answer 1 · 2017-02-10T12:01:50

See the entire solution process below:

First, expand the terms in parenthesis on each side of the equation:

#(4 xx x) + (4 xx 0.5) = (2 xx x) - (2 1.5)#

#4x + 2 = 2x - 3#

Next, subtract #color(red)(2)# and #color(blue)(2x)# from each side of the equation to isolate the #x# term while keeping the equation balanced:

#4x + 2 - color(red)(2) - color(blue)(2x) = 2x - 3 - color(red)(2) - color(blue)(2x)#

#4x - color(blue)(2x) + 2 - color(red)(2) = 2x - color(blue)(2x) - 3 - color(red)(2)#

#2x + 0 = 0 - 5#

#2x = -5#

Now, divide each side of the equation by #color(red)(2)# to solve for #x# while keeping the equation balanced:

#(2x)/color(red)(2) = -5/color(red)(2)#

#(color(red)(cancel(color(black)(2)))x)/cancel(color(red)(2)) = -2.5#

#x -2.5#