How do you solve #2j/7 - 1/7 = 3/14#?

1 Answer
Jul 14, 2015

Answer:

Rewrite with a common denominator or multiply through to remove the denominators then solve using standard arithmetic manipulations.

Explanation:

Note that there are two possible answers depending upon the interpretation of #2j/7#

Interpretation 1 : #2j/7# is intended to be a multiplication: #2(j/7)#
#2(j/7) - 1/7 = 3/14#
If we multiply all terms on both sides by #14# we get
#color(white)("XXXX")##4j - 2 = 3#
#color(white)("XXXX")##rarr j = 5/4#

Interpretation 2: #2j/7# is intended to be a mixed fraction#2+(j/7)#
(It is unusual, but not impossible, that a variable is part of a mixed fraction).

#2+(j/7) - 1/7 = 3/14#
Again, if we multiply all terms on both sides by #14# we get
#color(white)("XXXX")##28 +2j -2 = 3#
#color(white)("XXXX")##rarr 2j+26 = 3#
#color(white)("XXXX")##rarr 2j = -23#
#color(white)("XXXX")##rarr j = -23/2#