How do you solve #1< 5 x - 9 < 6#?

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Answer 1 · 2017-05-19T16:36:10

See a solution process below:

First, add #color(red)(9)# to each segment of the system of inequalities to isolate the #x# term while keeping the system balanced:

#1 + color(red)(9) < 5x - 9 + color(red)(9) < 6 + color(red)(9)#

#10 < 5x - 0 < 15#

#10 < 5x < 15#

Now, divide each segment by #color(red)(5)# to solve for #x# while keeping the system balanced:

#10/color(red)(5) < (5x)/color(red)(5) < 15/color(red)(5)#

#2 < (color(red)(cancel(color(black)(5)))x)/cancel(color(red)(5)) < 3#

#2 < x < 3#

Or

#x > 2# and #x < 3#

Or, in interval notation:

#(2, 3)#