How do you solve #\frac { 2x } { 3} - 2< x - 4#?

1 Answer
smendyka
Oct 5, 2017

See a solution process below:

Explanation:

First, subtract #color(red)((2x)/3)# and add #color(blue)(4)# to each side of the inequality to isolate the #x# term while keeping the inequality balanced:

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

#0 + 2 < -color(red)((2x)/3) + 1x - 0#

#2 < -color(red)((2x)/3) + 3/3x#

#2 < (-color(red)(2/3) + 3/3)x#

#2 < 1/3x#

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

#color(red)(3) xx 2 < color(red)(3) xx 1/3x#

#6 < cancel(color(red)(3)) xx 1/color(red)(cancel(color(black)(3)))x#

#6 < x#

To state the solution in terms of #x# we can reverse or "flip" the entire inequality:

#x > 6#

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