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

Question

Eli Assouline · Accepted Answer

#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#

Hazel Anglin · Answer

undefined To solve the equation -\frac { 1} { 2} = \frac { 2} { 3} y - \frac { 4} { 7}, we can follow these steps:

1. Start by isolating the variable term. In this case, we have the term \frac { 2} { 3} y on one side of the equation. To isolate it, we can move the constant term \frac { 4} { 7} to the other side.

2. To move \frac { 4} { 7} to the other side, we need to subtract it from both sides of the equation. This gives us:

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

3. Simplify the left side of the equation by finding a common denominator for \frac { 1} { 2} and \frac { 4} { 7}. The common denominator is 14, so we have:

-\frac { 7} { 14} + \frac { 8} { 14} = \frac { 2} { 3} y

4. Combine the fractions on the left side of the equation:

\frac { 1} { 14} = \frac { 2} { 3} y

5. To isolate y, we need to get rid of the coefficient \frac { 2} { 3}. We can do this by multiplying both sides of the equation by the reciprocal of \frac { 2} { 3}, which is \frac { 3} { 2}:

\frac { 1} { 14} \cdot \frac { 3} { 2} = \frac { 2} { 3} y \cdot \frac { 3} { 2}

6. Simplify both sides of the equation:

\frac { 3} { 28} = y

7. Therefore, the solution to the equation -\frac { 1} { 2} = \frac { 2} { 3} y - \frac { 4} { 7} is y = \frac { 3} { 28}.