Question

What is y in the equation 2/3 (2y+1) = 3/7 (2-y)

Answer 1

Answer:

$y=\frac{4}{37}$

Step-by-step explanation:

$\frac{2}{3}(2y+1)=\frac{3}{7}(2-y)$

$\frac{4}{3}y+\frac{2}{3} =\frac{6}{7}- \frac{3}{7}y$

Add $\frac{3}{7}y$ on both sides and subtract $\frac{2}{3}$ on both sides.

$(\frac{3}{7}y- \frac{2}{3})+\frac{4}{3}y+\frac{2}{3} =\frac{6}{7}- \frac{3}{7}y+(\frac{3}{7}y- \frac{2}{3})$

$\frac{3}{7}y+\frac{4}{3}y=\frac{6}{7}-\frac{2}{3}$

Solve the fractions.

$\frac{(3)(3)+(7)(4)}{(7)(3)}y=\frac{(6)(3)-(7)(2)}{(7)(3)}$

$\frac{9+28}{21} y=\frac{18-14}{21}$

$\frac{37}{21}y =\frac{4}{21}$

Multiply by the reciprocal of the fraction with the variable to isolate the variable. The reciprocal is the inverted fraction.

$\frac{21}{37}*\frac{37}{21}y =\frac{4}{21}*\frac{21}{37}$

$y=\frac{4}{37}$

Answer 2

first u have to distribute

4/3y+2/3= 6/7-3/7y

now subtract 2/3 on both sides

4/3y+2/3-2/3=6/7- 2/3-3/7y

4/3y= 6/7- 2/3-3/7y

u need to have common denominator

-2/3= - 14/21

6/7=18/21

18/21-14/21= 4/21

4/3y=4/21-3/7y

add 3/7y to both sides

u need to have common denominator

4/3y= 28/21y

3/7y= 9/21y

28/21y+9/21y= 37/21y

37/21y= 4/21

multiply 21/37 to both sides

37/21y times 21/37= 4/21 times 21/37

• y=84/777
• y= 9/111
• y=3/37