How do you solve #8x+9=2x+12#?

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Answer 1 · 2018-05-18T13:31:22

#x=0.5#

Given: #8x+9=2x+12#.

Subtract #12# from both sides.

#8x+9-12=2x+color(red)cancelcolor(black)12-color(red)cancelcolor(black)12#

#8x-3=2x#

Subtract #2x# from both sides.

#8x-2x-3=color(red)cancelcolor(black)(2x)-color(red)cancelcolor(black)(2x)#

#6x-3=0#

Add #3# to both sides.

#6x-color(red)cancelcolor(black)3+color(red)cancelcolor(black)3=3#

#6x=3#

#:.x=3/6=0.5#

Answer 2 · 2018-05-18T13:32:12

See a solution process below:

First, subtract #color(red)(9)# and #color(blue)(2x)# from each side of the equation to isolate the #x# term while keeping the equation balanced:

#8x - color(blue)(2x) + 9 - color(red)(9) = 2x - color(blue)(2x) + 12 - color(red)(9)#

#(8 - color(blue)(2))x + 0 = 0 + 3#

#6x = 3#

Now, divide each side of the equation by #color(red)(6)# to solve for #x# while keeping the equation balanced:

#(6x)/color(red)(6) = 3/color(red)(6)#

#(color(red)(cancel(color(black)(6)))x)/cancel(color(red)(6)) = 1/2#

#x = 1/2#