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

1 Answer
Jan 7, 2017

Answer:

See full solution process below

Explanation:

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#