How do you solve #-5< 2( x - 4) \leq 6#?

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Answer 1 · 2017-03-29T19:11:32

See the entire solution process below:

First, expand the term in parenthesis by multiplying each term in parenthesis by the term outside the parenthesis;

#-5 < (2 xx x) - (2 xx 4) <= 6#

#-5 < 2x - 8 <= 6#

Next, add #color(red)(8)# to each segment of the inequality to isolate the #x# term while keeping the system of inequalities balanced;

#-5 + color(red)(8) < 2x - 8 + color(red)(8) <= 6 + color(red)(8)#

#3 < 2x - 0 <= 14#

#3 < 2x <= 14#

Next, divide each segment of the system by #color(red)(2)# to solve for #x# while keeping the inequalities balanced:

#3/color(red)(2) < (2x)/color(red)(2) <= 14/color(red)(2)#

#3/2 < (color(red)(cancel(color(black)(2)))x)/cancel(color(red)(2)) <= 7#

#3/2 < x <= 7#