How do you solve #3b-6>=15+24b#?

1 Answer
May 29, 2017

Answer:

See a solution process below:

Explanation:

First, subtract #color(red)(3b)# and #color(blue)(15)# from each side of the inequality to isolate the #b# term while keeping the inequality balanced:

#3b - 6 - color(red)(3b) - color(blue)(15) >= 15 + 24b - color(red)(3b) - color(blue)(15)#

#3b - color(red)(3b) - 6 - color(blue)(15) >= 15 - color(blue)(15) + 24b - color(red)(3b)#

#0 - 21 >= 0 + (24 - color(red)(3))b#

#-21 >= 21b#

Now, divide each side of the inequality by #color(red)(21)# to solve for #b# while keeping the inequality balanced:

#-21/color(red)(21) >= (21b)/color(red)(21)#

#-1 >= (color(red)(cancel(color(red)(21)))b)/cancel(color(red)(21))#

#-1 >= b#

To state the solution in terms of #b# we can reverse or "flip" the entire inequality:

#b <= -1#