How do you solve #5x + 150= 0.5x + 105#?

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Answer 1 · 2017-05-06T01:40:11

See a solution process below:

First, subtract #color(red)(150)# and #color(blue)(0.5x)# from each side of the equation to isolate the #x# term while keeping the equation balanced:

#5x + 150 - color(red)(150) - color(blue)(0.5x) = 0.5x + 105 - color(red)(150) - color(blue)(0.5x)#

#5x - color(blue)(0.5x) + 150 - color(red)(150) = 0.5x - color(blue)(0.5x) + 105 - color(red)(150)#

#(5 - color(blue)(0.5))x + 0 = 0 - 45#

#4.5x = -45#

Now, divide each side of the equation by #color(red)(4.5)# to solve for #x# while keeping the equation balanced:

#(4.5x)/color(red)(4.5) = -45/color(red)(4.5)#

#(color(red)(cancel(color(black)(4.5)))x)/cancel(color(red)(4.5)) = -10#

#x = -10#