#3|6m -4|<=12#
Let start by dividing both sides by #color(red)(3)#
#(cancel3(|6m -4|))/cancelcolor(red)(3) <= 12/color(red)(3)#
#|6m - 4| <= 4#
We know...
#6m - 4<=4 and 6m - 4>= -4#
Let start with the first condition
#6m - 4 <=4#
Add #color(red)(4)# to both sides
#6m cancel(- 4) cancelcolor(red)(+4) <= 4 color(red)(+4)#
#6m <=8#
Divide both sides by #color(red)(6)# to find #m#
#(cancel6 m)/cancelcolor(red)(6) <= 8/color(red)(6)#
#m <= 4/3#
Now let solve the second condition
#6m - 4 >= -4#
Add #color(red)(4)# to both sides
#6m cancel(-4) cancelcolor(red)(+4) >= cancel(-4) cancelcolor(red)(+4)#
#6m >= 0#
Divide both sides by #color(red)(6)#
#(cancel6m)/cancelcolor(red)(6) >= 0/color(red)(6)#
#m >=0#
Thus,
the final answers are #m <=4/3 and m>=0#
