How do you solve and graph #-7<6x-1<5#?

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Answer 1 · 2017-08-08T02:44:48

See a solution process below:

First, add #color(red)(1)# to each segment of the system of inequalities to isolate the #x# term while keeping the system balanced:

#-7 + color(red)(1) < 6x - 1 + color(red)(1) < 5 + color(red)(1)#

#-6 < 6x - 0 < 6#

#-6 < 6x < 6#

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

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

#-1 < (color(red)(cancel(color(black)(6)))x)/cancel(color(red)(6)) < 1#

#-1 < x < 1#

Or

#x > -1# and #x < 1#

Or, in interval notation:

#(-1, 1)#

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