How do you solve #5( 6- 2b ) \geq 8b - 96#?

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Answer 1 · 2017-03-11T18:42:37

See the entire solution process below:

First, expand the terms in parenthesis on the left side of the inequality by multiplying each term within the parenthesis by #color(red)(5)#:

#color(red)(5)(6 - 2b) >= 8b - 96#

#(color(red)(5) xx 6) - (color(red)(5) xx 2b) >= 8b - 96#

#30 - 10b >= 8b - 96#

Next, add #color(red)(10b)# and #color(blue)(96)# to each side of the inequality to isolate the #b# term while keeping the inequality balanced:

#30 - 10b + color(red)(10b) + color(blue)(96) >= 8b - 96 + color(red)(10b) + color(blue)(96)#

#30 + color(blue)(96) - 10b + color(red)(10b) >= 8b + color(red)(10b) - 96 + color(blue)(96)#

#126 - 0 >= 18b - 0#

#126 >= 18b#

Now, divide each side of the inequality by #color(red)(18)# to solve for #b# while keeping the inequality balanced:

#126/color(red)(18) >= (18b)/color(red)(18)#

#7 >= (color(red)(cancel(color(black)(18)))b)/cancel(color(red)(18))#

#7 >= b#

To state this in terms of #b# we need to reverse or "flip" the inequality:

#b <= 7#