Solve the equation: $$\frac { 5 } { 4 } y - \frac { 1 } { 3 } = \frac { 1 } { 2 } ( 3 y - 1 ) .$$
A) $y = \frac { 2 } { 3 }$
B) $y = - 10$
C) $y = 0$
D) $y = \frac { 68 } { 201 }$

Question

Solve the equation: $$\frac { 5 } { 4 } y - \frac { 1 } { 3 } = \frac { 1 } { 2 } ( 3 y - 1 ) .$$ 
A) $y = \frac { 2 } { 3 }$
B) $y = - 10$
C) $y = 0$
D) $y = \frac { 68 } { 201 }$

Quizplus · Accepted Answer

To solve the equation, first distribute the $\frac{1}{2}$ on the right side: $$\frac{5}{4}y - \frac{1}{3} = \frac{3y}{2} - \frac{1}{2}.$$ Then, get all the y terms on one side and the constants on the other: $$\frac{5}{4}y - \frac{3y}{2} = -\frac{1}{2} + \frac{1}{3}.$$ To simplify, find a common denominator for the y terms and the constants: $$\frac{10y - 12y}{8} = \frac{-3 + 2}{6},$$ which simplifies to $$-\frac{2y}{8} = -\frac{1}{6}.$$ Simplifying further gives $$-\frac{y}{4} = -\frac{1}{6},$$ and solving for y gives $y = \frac{2}{3}.$

Solve the Equation 54y−13=12(3y−1).\frac { 5 } { 4 } y - \frac { 1 } { 3 } = \frac { 1 } { 2 } ( 3 y - 1 ) .45​y−31​=21​(3y−1).

Solve the Equation $\frac { 5 } { 4 } y - \frac { 1 } { 3 } = \frac { 1 } { 2 } ( 3 y - 1 ) .$