Solve for y 4y-1/2=-1/2y+1/4

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

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

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

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

Add $\frac{y}{2}$ to both sides of the equation.

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

To write $4 y$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Combine $4 y$ and $\frac{2}{2}$ .

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

Combine the numerators over the common denominator.

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

Combine the numerators over the common denominator.

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

Multiply $2$ by $4$ .

$\frac{8 y + y - 1}{2} = \frac{1}{4}$

Add $8 y$ and $y$ .

$\frac{9 y - 1}{2} = \frac{1}{4}$

Multiply both sides by $2$ .

$\frac{9 y - 1}{2} \cdot 2 = \frac{1}{4} \cdot 2$

Simplify.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{9 y - 1}{2} \cdot 2 = \frac{1}{4} \cdot 2$

Rewrite the expression.

$9 y - 1 = \frac{1}{4} \cdot 2$

Simplify the right side.

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$9 y - 1 = \frac{1}{2 (2)} \cdot 2$

Cancel the common factor.

$9 y - 1 = \frac{1}{2 \cdot 2} \cdot 2$

Rewrite the expression.

$9 y - 1 = \frac{1}{2}$

Solve for $y$ .

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

Add $1$ to both sides of the equation.

$9 y = \frac{1}{2} + 1$

Write $1$ as a fraction with a common denominator.

$9 y = \frac{1}{2} + \frac{2}{2}$

Combine the numerators over the common denominator.

$9 y = \frac{1 + 2}{2}$

Add $1$ and $2$ .

$9 y = \frac{3}{2}$

Divide each term in $9 y = \frac{3}{2}$ by $9$ and simplify.

Divide each term in $9 y = \frac{3}{2}$ by $9$ .

$\frac{9 y}{9} = \frac{\frac{3}{2}}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 y}{9} = \frac{\frac{3}{2}}{9}$

Divide $y$ by $1$ .

$y = \frac{\frac{3}{2}}{9}$

Simplify the right side.

Multiply the numerator by the reciprocal of the denominator.

$y = \frac{3}{2} \cdot \frac{1}{9}$

Cancel the common factor of $3$ .

Factor $3$ out of $9$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

Multiply $2$ by $3$ .

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

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$y = 0.1\overline{6}$

Solve for y 4y-1/2=-1/2y+1/4

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