Solve for y 5/4y-1/3=1/2(3y-1)

$\frac{5}{4} y - \frac{1}{3} = \frac{1}{2} (3 y - 1)$

Step 1

Combine $\frac{5}{4}$ and $y$ .

$\frac{5 y}{4} - \frac{1}{3} = \frac{1}{2} \cdot (3 y - 1)$

Step 2

Simplify $\frac{1}{2} \cdot (3 y - 1)$ .

Apply the distributive property.

$\frac{5 y}{4} - \frac{1}{3} = \frac{1}{2} (3 y) + \frac{1}{2} \cdot - 1$

Multiply $\frac{1}{2} (3 y)$ .

Combine $3$ and $\frac{1}{2}$ .

$\frac{5 y}{4} - \frac{1}{3} = \frac{3}{2} y + \frac{1}{2} \cdot - 1$

Combine $\frac{3}{2}$ and $y$ .

$\frac{5 y}{4} - \frac{1}{3} = \frac{3 y}{2} + \frac{1}{2} \cdot - 1$

Combine $\frac{1}{2}$ and $- 1$ .

$\frac{5 y}{4} - \frac{1}{3} = \frac{3 y}{2} + \frac{- 1}{2}$

Move the negative in front of the fraction.

$\frac{5 y}{4} - \frac{1}{3} = \frac{3 y}{2} - \frac{1}{2}$

Step 3

Move all terms containing $y$ to the left side of the equation.

Subtract $\frac{3 y}{2}$ from both sides of the equation.

$\frac{5 y}{4} - \frac{1}{3} - \frac{3 y}{2} = - \frac{1}{2}$

To write $- \frac{3 y}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{5 y}{4} - \frac{3 y}{2} \cdot \frac{2}{2} - \frac{1}{3} = - \frac{1}{2}$

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{3 y}{2}$ by $\frac{2}{2}$ .

$\frac{5 y}{4} - \frac{3 y \cdot 2}{2 \cdot 2} - \frac{1}{3} = - \frac{1}{2}$

Multiply $2$ by $2$ .

$\frac{5 y}{4} - \frac{3 y \cdot 2}{4} - \frac{1}{3} = - \frac{1}{2}$

Combine the numerators over the common denominator.

$\frac{5 y - 3 y \cdot 2}{4} - \frac{1}{3} = - \frac{1}{2}$

Simplify each term.

Simplify the numerator.

Factor $y$ out of $5 y - 3 y \cdot 2$ .

Factor $y$ out of $5 y$ .

$\frac{y \cdot 5 - 3 y \cdot 2}{4} - \frac{1}{3} = - \frac{1}{2}$

Factor $y$ out of $- 3 y \cdot 2$ .

$\frac{y \cdot 5 + y (- 3 \cdot 2)}{4} - \frac{1}{3} = - \frac{1}{2}$

Factor $y$ out of $y \cdot 5 + y (- 3 \cdot 2)$ .

$\frac{y (5 - 3 \cdot 2)}{4} - \frac{1}{3} = - \frac{1}{2}$

Multiply $- 3$ by $2$ .

$\frac{y (5 - 6)}{4} - \frac{1}{3} = - \frac{1}{2}$

Subtract $6$ from $5$ .

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

Move $- 1$ to the left of $y$ .

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

Move the negative in front of the fraction.

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

Step 4

Move all terms not containing $y$ to the right side of the equation.

Add $\frac{1}{3}$ to both sides of the equation.

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

To write $- \frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

To write $\frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{2}$ by $\frac{3}{3}$ .

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

Multiply $2$ by $3$ .

$- \frac{y}{4} = - \frac{3}{6} + \frac{1}{3} \cdot \frac{2}{2}$

Multiply $\frac{1}{3}$ by $\frac{2}{2}$ .

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

Multiply $3$ by $2$ .

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

Combine the numerators over the common denominator.

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

Add $- 3$ and $2$ .

$- \frac{y}{4} = \frac{- 1}{6}$

Move the negative in front of the fraction.

$- \frac{y}{4} = - \frac{1}{6}$

Step 5

Multiply both sides of the equation by $- 4$ .

$- 4 (- \frac{y}{4}) = - 4 (- \frac{1}{6})$

Step 6

Simplify both sides of the equation.

Simplify the left side.

Simplify $- 4 (- \frac{y}{4})$ .

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{y}{4}$ into the numerator.

$- 4 \frac{- y}{4} = - 4 (- \frac{1}{6})$

Factor $4$ out of $- 4$ .

$4 (- 1) \frac{- y}{4} = - 4 (- \frac{1}{6})$

Cancel the common factor.

$4 \cdot - 1 \frac{- y}{4} = - 4 (- \frac{1}{6})$

Rewrite the expression.

$- - y = - 4 (- \frac{1}{6})$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 y = - 4 (- \frac{1}{6})$

Multiply $y$ by $1$ .

$y = - 4 (- \frac{1}{6})$

Simplify the right side.

Simplify $- 4 (- \frac{1}{6})$ .

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{1}{6}$ into the numerator.

$y = - 4 (\frac{- 1}{6})$

Factor $2$ out of $- 4$ .

$y = 2 (- 2) \frac{- 1}{6}$

Factor $2$ out of $6$ .

$y = 2 \cdot - 2 \frac{- 1}{2 \cdot 3}$

Cancel the common factor.

$y = 2 \cdot - 2 \frac{- 1}{2 \cdot 3}$

Rewrite the expression.

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

Combine $- 2$ and $\frac{- 1}{3}$ .

$y = \frac{- 2 \cdot - 1}{3}$

Multiply $- 2$ by $- 1$ .

$y = \frac{2}{3}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$y = \frac{2}{3}$

Decimal Form:

$y = 0.\overline{6}$

Solve for y 5/4y-1/3=1/2(3y-1)

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