How do you solve #-\frac { 1} { 2} + y = - \frac { 3} { 7}#?

1 Answer
Jim G.
Dec 10, 2016

#y=1/14#

Explanation:

To 'eliminate' the fractions on both sides of the equation, multiply ALL terms by the #color(blue)"lowest common multiple"# (LCM) of the denominators 2 and 7. This is 14

#(cancel(14)^7xx-1/cancel(2)^1)+(14xxy)=(cancel(14)^2xx-3/cancel(7)^1)#

#rArr(7xx-1)+14y=(2xx-3)#

#rArr-7+14y=-6larr" no fractions"#

leave 14y on left side of equation and collect numeric values on the right side.

add 7 to both sides of the equation.

#cancel(-7)cancel(+7)+14y=-6+7#

#rArr14y=1#

To solve for y, divide both sides by 14

#(cancel(14) y)/cancel(14)=1/14#

#rArry=1/14" is the solution"#

#color(blue)"Check solution"#

#"left side " = -1/2+1/14#

#=-7/14+1/14=-6/14=-3/7=" right side " ✔︎#

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