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

Question

Hazel Anglin · Accepted Answer

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

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#

Julia Adams · Answer

undefined To solve the equation 2j/7 - 1/7 = 3/14, you first need to isolate the variable j. Start by adding 1/7 to both sides of the equation to get rid of the -1/7 term. This gives you 2j/7 = 3/14 + 1/7. Then, combine the fractions on the right side to get a common denominator, which is 14. So, 3/14 + 1/7 becomes 6/14. Now, your equation is 2j/7 = 6/14. To isolate j, multiply both sides of the equation by the reciprocal of 2/7, which is 7/2. This cancels out the fraction on the left side, leaving you with j = (6/14) * (7/2). Simplify this expression to find the value of j.