How do you solve #3/(x-7)=2/(4x+1)# and check for extraneous solutions?

1 Answer
Lil Del
Oct 19, 2016

The solution of the equation is #x = -1.7#, and it is not extraneous.

Explanation:

To solve this proportion, begin by cross multiplying. This will give you an equation in familiar form.

#3/(x - 7) = 2/(4x + 1)#
#3(4x + 1) = 2(x - 7)#
#12x + 3 = 2x - 14#
#12x - 2x + 3 = 2x - 2x - 14#
#10x + 3 = -14#
#10x + 3 - 3 = -14 - 3#
#10x = -17#
#10x/10 = -17/10#
#x = -1.7#

To check whether the solution is extraneous, substitute #-1.7# for #x# in the original equation to see whether the two sides of the equation are equal. If they are, the answer is a solution. If they are not, the answer is an extraneous solution.

#3/(-1.7 - 7) = 2/(4*-1.7 + 1) #3/-8.7 = 2/(-6.8 + 1)
#3/-8.7 = 2/-5.8#
#-0.3448275862 = -0.3448275862#

Since the equation is true, #-1.7# is a solution.

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