Solve for x 2x+4y=6y+1/2x

$2 x + 4 y = 6 y + \frac{1}{2} x$

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

$2 x + 4 y = 6 y + \frac{x}{2}$

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

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

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

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

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

Combine $2 x$ and $\frac{2}{2}$ .

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

Combine the numerators over the common denominator.

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

Simplify each term.

Simplify the numerator.

Factor $x$ out of $2 x \cdot 2 - x$ .

Factor $x$ out of $2 x \cdot 2$ .

$4 y + \frac{x (2 \cdot 2) - x}{2} = 6 y$

Factor $x$ out of $- x$ .

$4 y + \frac{x (2 \cdot 2) + x \cdot - 1}{2} = 6 y$

Factor $x$ out of $x (2 \cdot 2) + x \cdot - 1$ .

$4 y + \frac{x (2 \cdot 2 - 1)}{2} = 6 y$

Multiply $2$ by $2$ .

$4 y + \frac{x (4 - 1)}{2} = 6 y$

Subtract $1$ from $4$ .

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

Move $3$ to the left of $x$ .

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

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

Subtract $4 y$ from both sides of the equation.

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

Subtract $4 y$ from $6 y$ .

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

Multiply both sides of the equation by $\frac{2}{3}$ .

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

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{2}{3} \cdot \frac{3 x}{2}$ .

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $3$ .

Factor $3$ out of $3 x$ .

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

Cancel the common factor.

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

Rewrite the expression.

$x = \frac{2}{3} (2 y)$

Simplify the right side.

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

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

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

Multiply $2$ by $2$ .

$x = \frac{4}{3} y$

Combine $\frac{4}{3}$ and $y$ .

$x = \frac{4 y}{3}$

Solve for x 2x+4y=6y+1/2x

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