How do you solve $-\frac { 1} { 2} = \frac { 2} { 3} y - \frac { 4} { 7}$ ?

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Answer 1 · 2017-03-01T08:25:51

$y = 3/28$

$-\frac { 1} { 2} = \frac { 2} { 3} y - \frac { 4} { 7}$

As soon as you have an EQUATION with fractions, you can get rid of the denominators immediately.

Multiply each term by the LCM of the denominators.
In this case it is $42$

$(color(blue)(42xx)-1)/2 = (color(blue)(42xx)2)/3y -(color(blue)(42xx)4)/7" "larr$ cancel

$(cancel(42)^21 xx-1)/cancel2 = (cancel(42)^14xx2)/cancel3y -(cancel(42)^6xx4)/cancel7$

$-21 =28y -24" "larr$ add 24 to both sides

$-21 +24 = 28y-24+24$

$3 = 28y$

$3/28 = y$

How do you solve -\frac { 1} { 2} = \frac { 2} { 3} y - \frac { 4} { 7}-\frac { 1} { 2} = \frac { 2} { 3} y - \frac { 4} { 7}?