How do you solve #-2v + 7< - 3#?

1 Answer
smendyka
Jan 2, 2017

You solve this inequality like an equality, except you need to be careful when multiplying or dividing an inequality by a negative. See full explanation below.

Explanation:

The first step is to subtract #color(red)(7)# from each side of the inequality to isolate the #v# term while keeping the inequality balanced:

#-2v + 7 - color(red)(7) < -3 - color(red)(7)#

#-2v + 0 < -10#

#-2v < -10#

Now we can divide each side of the inequality by #color(red)(-2)# to solve for #v# while keeping the equation balanced.

However, because this is an inequality and because we are multiplying or dividing by a negative number we need to reverse the inequality:

#(-2v)/color(red)(-2) > (-10)/color(red)(-2)#

#(color(red)(cancel(color(black)(-2)))v)/cancel(color(red)(-2)) > 5#

#v > 5#

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