How do you solve and check your solutions to #-5.3=2.2v-8.6#?

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Answer 1 · 2017-01-31T22:55:06

See the entire solution and validation process below:

First, add #color(red)(8.6)# to the equation to isolate the #v# term while keeping the equation balanced:

#-5.3 + color(red)(8.6) = 2.2v - 8.6 + color(red)(8.6)#

#3.3 = 2.2v - 0#

#3.3 = 2.2v#

Now, divide each side of the equation by #color(red)(2.2)# to solve for #v# while keeping the equation balanced:

#3.3/color(red)(2.2) = (2.2v)/color(red)(2.2)#

#(3 xx 1.1)/(2 xx 1.1) = (color(red)(cancel(color(black)(2.2)))v)/cancel(color(red)(2.2))#

#(3 xx cancel(1.1))/(2 xx cancel(1.1)) = v#

#3/2 = v#

#v = 3/2#

Now to check the solution substitute #3/2# for #v# and calculate the right side of the equation and ensure it is equal #-5.3#

#-5.3 = (2.2 xx 3/2) - 8.6#

#-5.3 = 3.3 - 8.6#

#-5.3 = -5.3#

Because both sides of the equation are equal #v = 3/2# is a valid solution.