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

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

Step 1

Simplify each term.

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

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

Move $2$ to the left of $x$ .

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

Step 2

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

Subtract $\frac{3}{7}$ from both sides of the equation.

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

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

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

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

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

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

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

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

Multiply $2$ by $7$ .

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

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

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

Multiply $7$ by $2$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $- 3$ by $2$ .

$- \frac{2 x}{3} = \frac{7 - 6}{14}$

Subtract $6$ from $7$ .

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

Step 3

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

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

Step 4

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{3}{2} (- \frac{2 x}{3})$ .

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{3}{2}$ into the numerator.

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

Move the leading negative in $- \frac{2 x}{3}$ into the numerator.

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

Factor $3$ out of $- 3$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $2$ .

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply.

Multiply $- 1$ by $- 1$ .

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

Multiply $x$ by $1$ .

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

Simplify the right side.

Multiply $- \frac{3}{2} \cdot \frac{1}{14}$ .

Multiply $\frac{1}{14}$ by $\frac{3}{2}$ .

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

Multiply $14$ by $2$ .

$x = - \frac{3}{28}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{3}{28}$

Decimal Form:

$x = - 0.10714285 \dots$

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

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