First, multiply the terms within parenthesis on each side of the inequality:
#(6 xx m) - (6 xx 3) > (5 xx 2m) + (5 xx 4)#
#6m - 18 > 10m + 20#
Next, subtract #color(red)(6m)# and #color(blue)(20)# from each side of the inequality to isolate the #m# term while keeping the inequality balanced:
#6m - 18 - color(red)(6m) - color(blue)(20) > 10m + 20 - color(red)(6m) - color(blue)(20)#
#6m - color(red)(6m) - 18 - color(blue)(20) > 10m - color(red)(6m) + 20 - color(blue)(20)#
#0 - 38 > 4m + 0#
#-38 > 4m#
Now, divide each side of the inequality by #color(red)(4)# to solve for #m# while keeping the inequality balanced:
#(-38)/color(red)(4) > (4m)/color(red)(4)#
#(2 xx -19)/(2 xx 2) > (color(red)(cancel(color(black)(4)))m)/cancel(color(red)(4))#
#(color(red)(cancel(color(black)(2))) xx -19)/(color(red)(cancel(color(black)(2))) xx 2) > (color(red)(cancel(color(black)(4)))m)/cancel(color(red)(4))#
#-19/2 > m#
To solve for #m# we need to reverse or "flip" the inequality:
#m < -19/2#
