How do you solve #-16x - 2< - 44- 10x#?

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Answer 1 · 2017-07-16T13:46:39

See a solution process below:

First, add #color(red)(16x)# and #color(blue)(44)# to each side of the inequality to isolate the #x# term while keeping the inequality balanced:

#-16x - 2 + color(red)(16x) + color(blue)(44) < -44 - 10x + color(red)(16x) + color(blue)(44)#

#-16x + color(red)(16x) - 2 + color(blue)(44) < -44 + color(blue)(44) - 10x + color(red)(16x)#

#0 + 42 < 0 + (-10 + color(red)(16))x#

#42 < 6x#

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

#42/color(red)(6) < (6x)/color(red)(6)#

#7 < (color(red)(cancel(color(black)(6)))x)/cancel(color(red)(6))#

#7 < x#

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

#x > 7#