How do you solve #-2+ 5( 7v - 8) \leq - 217#?

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Answer 1 · 2017-05-17T17:57:57

See a solution process below:

First, add #color(red)(2)# to each side of the inequality to isolate the term in parenthesis while keeping the inequality balanced:

#color(red)(2) - 2 + 5(7v - 8) <= color(red)(2) - 217#

#0 + 5(7v - 8) <= -215#

#5(7v - 8) <= -215#

Next, divide each side of the inequality by #color(red)(5)# to eliminate the need for the parenthesis while keeping the inequality balanced:

#(5(7v - 8))/color(red)(5) <= -215/color(red)(5)#

#(color(red)(cancel(color(black)(5)))(7v - 8))/cancel(color(red)(5)) <= -43#

#7v - 8 <= -43#

Then, add #color(red)(8)# to each side of the inequality to isolate the #v# term while keeping the inequality balanced:

#7v - 8 + color(red)(8) <= -43 + color(red)(8)#

#7v - 0 <= -35#

#7v <= -35#

Now, divide each side of the inequality by #color(red)(7)# to solve for #v# while keeping the inequality balanced:

#(7v)/color(red)(7) <= -35/color(red)(7)#

#(color(red)(cancel(color(black)(7)))v)/cancel(color(red)(7)) <= -5#

#v <= -5#