Solve for x 3/7=1/2-1/2x

$\frac{3}{7} = \frac{1}{2} - \frac{1}{2} x$

Rewrite the equation as $\frac{1}{2} - \frac{1}{2} x = \frac{3}{7}$ .

$\frac{1}{2} - \frac{1}{2} x = \frac{3}{7}$

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

$\frac{1}{2} - \frac{x}{2} = \frac{3}{7}$

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

Subtract $\frac{1}{2}$ from both sides of the equation.

$- \frac{x}{2} = \frac{3}{7} - \frac{1}{2}$

To write $\frac{3}{7}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{x}{2} = \frac{3}{7} \cdot \frac{2}{2} - \frac{1}{2}$

To write $- \frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$- \frac{x}{2} = \frac{3}{7} \cdot \frac{2}{2} - \frac{1}{2} \cdot \frac{7}{7}$

Write each expression with a common denominator of $14$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{3}{7}$ by $\frac{2}{2}$ .

$- \frac{x}{2} = \frac{3 \cdot 2}{7 \cdot 2} - \frac{1}{2} \cdot \frac{7}{7}$

Multiply $7$ by $2$ .

$- \frac{x}{2} = \frac{3 \cdot 2}{14} - \frac{1}{2} \cdot \frac{7}{7}$

Multiply $\frac{1}{2}$ by $\frac{7}{7}$ .

$- \frac{x}{2} = \frac{3 \cdot 2}{14} - \frac{7}{2 \cdot 7}$

Multiply $2$ by $7$ .

$- \frac{x}{2} = \frac{3 \cdot 2}{14} - \frac{7}{14}$

Combine the numerators over the common denominator.

$- \frac{x}{2} = \frac{3 \cdot 2 - 7}{14}$

Simplify the numerator.

Multiply $3$ by $2$ .

$- \frac{x}{2} = \frac{6 - 7}{14}$

Subtract $7$ from $6$ .

$- \frac{x}{2} = \frac{- 1}{14}$

Move the negative in front of the fraction.

$- \frac{x}{2} = - \frac{1}{14}$

Multiply both sides of the equation by $- 2$ .

$- 2 (- \frac{x}{2}) = - 2 (- \frac{1}{14})$

Simplify both sides of the equation.

Simplify the left side.

Simplify $- 2 (- \frac{x}{2})$ .

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{x}{2}$ into the numerator.

$- 2 \frac{- x}{2} = - 2 (- \frac{1}{14})$

Factor $2$ out of $- 2$ .

$2 (- 1) \frac{- x}{2} = - 2 (- \frac{1}{14})$

Cancel the common factor.

$2 \cdot - 1 \frac{- x}{2} = - 2 (- \frac{1}{14})$

Rewrite the expression.

$- - x = - 2 (- \frac{1}{14})$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 x = - 2 (- \frac{1}{14})$

Multiply $x$ by $1$ .

$x = - 2 (- \frac{1}{14})$

Simplify the right side.

Simplify $- 2 (- \frac{1}{14})$ .

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{1}{14}$ into the numerator.

$x = - 2 (\frac{- 1}{14})$

Factor $2$ out of $- 2$ .

$x = 2 (- 1) \frac{- 1}{14}$

Factor $2$ out of $14$ .

$x = 2 \cdot - 1 \frac{- 1}{2 \cdot 7}$

Cancel the common factor.

$x = 2 \cdot - 1 \frac{- 1}{2 \cdot 7}$

Rewrite the expression.

$x = - \frac{- 1}{7}$

Move the negative in front of the fraction.

$x = - - \frac{1}{7}$

Multiply $- - \frac{1}{7}$ .

Multiply $- 1$ by $- 1$ .

$x = 1 (\frac{1}{7})$

Multiply $\frac{1}{7}$ by $1$ .

$x = \frac{1}{7}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1}{7}$

Decimal Form:

$x = 0.\overline{142857}$

Solve for x 3/7=1/2-1/2x

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