How do you solve #5<2x+7<13#?

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Answer 1 · 2017-01-07T19:17:54

See full solution process below

While solving this set of inequalities we need to perform each operation to all three parts of the set of inequalities to keep everything balanced.

First, subtract #color(red)(7) from each term in the inequalities:

#5 - color(red)(7) < 2x + 7 - color(red)(7) < 13 - color(red)(7)#

#-2 < 2x + 0 < 6#

#-2 < 2x < 6#

Now, we can divide each portion of the inequalities by #color(red)(2)# to solve for #x# while keeping the inequality set balanced:

#(-2)/color(red)(2) < (2x)/color(red)(2) < 6/color(red)(2)#

#-1 < (color(red)(cancel(color(black)(2)))x)/cancel(color(red)(2)) < 3#

#-1 < x < 3#