Answer:
[tex]y=\frac{4}{37}[/tex]
Step-by-step explanation:
[tex]\frac{2}{3}(2y+1)=\frac{3}{7}(2-y)[/tex]
[tex]\frac{4}{3}y+\frac{2}{3} =\frac{6}{7}- \frac{3}{7}y[/tex]
Add [tex]\frac{3}{7}y[/tex] on both sides and subtract [tex]\frac{2}{3}[/tex] on both sides.
[tex](\frac{3}{7}y- \frac{2}{3})+\frac{4}{3}y+\frac{2}{3} =\frac{6}{7}- \frac{3}{7}y+(\frac{3}{7}y- \frac{2}{3})[/tex]
[tex]\frac{3}{7}y+\frac{4}{3}y=\frac{6}{7}-\frac{2}{3}[/tex]
Solve the fractions.
[tex]\frac{(3)(3)+(7)(4)}{(7)(3)}y=\frac{(6)(3)-(7)(2)}{(7)(3)}[/tex]
[tex]\frac{9+28}{21} y=\frac{18-14}{21}[/tex]
[tex]\frac{37}{21}y =\frac{4}{21}[/tex]
Multiply by the reciprocal of the fraction with the variable to isolate the variable. The reciprocal is the inverted fraction.
[tex]\frac{21}{37}*\frac{37}{21}y =\frac{4}{21}*\frac{21}{37}[/tex]
[tex]y=\frac{4}{37}[/tex]
