How do you solve #3/5 (x-12) >x-24#?

1 Answer
Feb 11, 2017

Answer:

See the entire solution process below:

Explanation:

First, expand the term in parenthesis on the left side of the inequality:

#(3/5 xx x) - (3/5 xx 12) > x - 24#

#3/5x - 36/5 > x - 24#

Next, subtract #color(red)(3/5x)# and add #color(blue)(24)# to each side of the inequality while keeping the inequality balanced:

#3/5x - 36/5 - color(red)(3/5x) + color(blue)(24) > x - 24 - color(red)(3/5x) + color(blue)(24)#

#3/5x - color(red)(3/5x) - 36/5 + color(blue)(24) > x - color(red)(3/5x) - 24 + color(blue)(24)#

#0 - 36/5 + (5/5 xx color(blue)(24)) > (5/5 xx x) - color(red)(3/5x) - 0#

#-36/5 + 120/5 > 5/5x - 3/5x#

#84/5 > 2/5x#

Now, multiply each side of the equation by #color(red)(5)/color(2)# to solve for #x# while keeping the equation balanced:

#color(red)(5)/color(blue)(2) xx 84/5 > color(red)(5)/color(blue)(2) xx 2/5x#

#cancel(color(red)(5))/color(blue)(2) xx 84/color(red)(cancel(color(black)(5))) > 10/10x#

#84/2 > 1x#

#42 > x#

Finally, to solve in terms of #x# we need to reverse or "flip" the inequality:

#x < 42#