First, expand the terms in parenthesis on the right side of the inequality by multiplying each term within the parenthesis by the term outside the parenthesis:
#6m - 6 < color(red)(2)(m + 6) + 1#
#6m - 6 < (color(red)(2) * m) + (color(red)(2) * 6) + 1#
#6m - 6 < 2m + 12 + 1#
#6m - 6 < 2m + 13#
Next, add #color(red)(6)# and subtract #color(blue)(2m)# from each side of the inequality to isolate the #m# term while keeping the inequality balanced:
#-color(blue)(2m) + 6m - 6 + color(red)(6) < -color(blue)(2m) + 2m + 13 + color(red)(6)#
#(-color(blue)(2) + 6)m - 0 < 0 + 19#
#4m < 19#
Now, divide each side of the inequality by #color(red)(4)# to solve for #m# while keeping the inequality balanced:
#(4m)/color(red)(4) < 19/color(red)(4)#
#(color(red)(cancel(color(black)(4)))m)/cancel(color(red)(4)) < 19/4#
#m < 19/4#
