The absolute value function takes any term and transforms it to its non-negative form. Therefore, we must solve the term within the absolute value function for both its negative and positive equivalent.
#-45 > 4x + 9 > 45#
First, subtract #color(red)(9)# from each segment of the system of inequalities to isolate the #x# term while keeping the system balanced:
#-45 - color(red)(9) > 4x + 9 - color(red)(9) > 45 - color(red)(9)#
#-54 > 4x + 0 > 36#
#-54 > 4x > 36#
Now, divide each segment by #color(red)(4)# to solve for #x# while keeping the system balanced:
#-54/color(red)(4) > (4x)/color(red)(4) > 36/color(red)(4)#
#(2 xx -27)/color(red)(2 xx 2) > (color(red)(cancel(color(black)(4)))x)/cancel(color(red)(4)) > 9#
#(color(red)(cancel(color(black)(2))) xx -27)/color(red)(color(black)(cancel(color(red)(2))) xx 2) > x > 9#
#-27/2 > x > 9#
Or
#x < -27/2# and #x > 9#
