How do you solve #-7\geq 6u - 43#?

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Answer 1 · 2018-01-12T22:36:03

See a solution process below:

First, add #color(red)(43)# to each side of the inequality to isolate the #u# term while keeping the inequality balanced:

#-7 + color(red)(43) >= 6u - 43 + color(red)(43)#

#36 >= 6u - 0#

#36 >= 6u#

Now, divide each side of the inequality by #color(red)(6)# to solve for #u# while keeping the inequality balanced:

#36/color(red)(6) >= (6u)/color(red)(6)#

#6 >= (color(red)(cancel(color(black)(6)))u)/cancel(color(red)(6))#

#6 >= u#

We can reverse or "flip" the entire inequality to state the solution in terms of #u#:

#u <= 6#