How do you solve #12x + 6\geq 9x + 12#?

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Answer 1 · 2018-01-16T23:44:39

See a solution process below:

First, subtract #color(red)(6)# and #color(blue)(9x)# from each side of the inequality to isolate the #x# term while keeping the inequality balanced:

#12x - color(blue)(9x) + 6 - color(red)(6) >= 9x - color(blue)(9x) + 12 - color(red)(6)#

#(12 - color(blue)(9))x + 0 >= 0 + 6#

#3x >= 6#

Now, divide each side of the inequality by #color(red)(3)# to solve for #x# while keeping the inequality balanced:

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

#(color(red)(cancel(color(black)(3)))x)/cancel(color(red)(3)) >= 2#

#x >= 2#