How do you solve #2x-3 > 11-5x#?

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Answer 1 · 2017-12-05T02:23:16

See a solution process below:

First, add #color(red)(3)# and #color(blue)(5x)# to each side of the inequality to isolate the #x# term while keeping the inequality balanced:

#2x - 3 + color(red)(3) + color(blue)(5x) > 11 - 5x + color(red)(3) + color(blue)(5x)#

#2x + color(blue)(5x) - 3 + color(red)(3) > 11 + color(red)(3) - 5x + color(blue)(5x)#

#(2 + color(blue)(5))x - 0 > 14 - 0#

#7x > 14#

Now, divide each side of the inequality by #color(red)(7)# to solve for #x# while keeping the inequality balanced:

#(7x)/color(red)(7) > 14/color(red)(7)#

#(color(red)(cancel(color(black)(7)))x)/cancel(color(red)(7)) > 2#

#x > 2#