First, expand the terms in parenthesis by multiplying each term within the parenthesis by the term outside the parenthesis:
#2x + 6 < color(red)(3)(x - 1) <= color(blue)(2)(x + 3)#
#2x + 6 < (color(red)(3) xx x) - (color(red)(3) xx 1) <= (color(blue)(2) xx x) + (color(blue)(2) xx 3)#
#2x + 6 < 3x - 3 <= 2x + 6#
Now, subtract #color(red)(2x)# from each segment of the systems of inequalities and add #color(blue)(3)# to each segment to solve for #x# while keeping the system balanced:
#-color(red)(2x) + 2x + 6 + color(blue)(3) < -color(red)(2x) + 3x - 3 + color(blue)(3) <= -color(red)(2x) + 2x + 6 + color(blue)(3)#
#9 < x <= 9#
There is no solution to this system of inequalities. There is not a number which is both greater than #9# and at the same time less than or equal to #9#.
Or, the solution is the empty or null set: #{O/}#
