How do you solve #6(m-3)>5(2m+4)#?

1 Answer
Feb 11, 2017

Answer:

See the entire solution process below:

Explanation:

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#