How do you solve and write the following in interval notation: #-2(x-1)-12<2(x+1)#?

1 Answer
smendyka
Jul 8, 2017

See a solution process below:

Explanation:

First, expand the terms on both sides of the inequality by multiplying each term within the parenthesis by the term outside the parenthesis:

#color(red)(-2)(x - 1) - 12 < color(blue)(2)(x + 1)#

#(color(red)(-2) xx x) - (color(red)(-2) xx 1) - 12 < (color(blue)(2) xx x) + (color(blue)(2) xx 1)#

#-2x - (-2) - 12 < 2x + 2#

#-2x + 2 - 12 < 2x + 2#

#-2x - 10 < 2x + 2#

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

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

#0 - 12 < (color(red)(x) + 2)x + 0#

#-12 < 4x#

Now, divide each side of the inequality by #color(red)(4)# to solve for #x# while keeping the inequality balanced:

#-12/color(red)(4) < (4x)/color(red)(4)#

#-3 < (color(red)(cancel(color(black)(4)))x)/cancel(color(red)(4))#

#-3 < x#

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