Solve for x 2/3-4x+7/2=-9x+5/6

$\frac{2}{3} - 4 x + \frac{7}{2} = - 9 x + \frac{5}{6}$

Simplify $\frac{2}{3} - 4 x + \frac{7}{2}$ .

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

$- 4 x + \frac{2}{3} \cdot \frac{2}{2} + \frac{7}{2} = - 9 x + \frac{5}{6}$

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

$- 4 x + \frac{2}{3} \cdot \frac{2}{2} + \frac{7}{2} \cdot \frac{3}{3} = - 9 x + \frac{5}{6}$

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

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

$- 4 x + \frac{2 \cdot 2}{3 \cdot 2} + \frac{7}{2} \cdot \frac{3}{3} = - 9 x + \frac{5}{6}$

Multiply $3$ by $2$ .

$- 4 x + \frac{2 \cdot 2}{6} + \frac{7}{2} \cdot \frac{3}{3} = - 9 x + \frac{5}{6}$

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

$- 4 x + \frac{2 \cdot 2}{6} + \frac{7 \cdot 3}{2 \cdot 3} = - 9 x + \frac{5}{6}$

Multiply $2$ by $3$ .

$- 4 x + \frac{2 \cdot 2}{6} + \frac{7 \cdot 3}{6} = - 9 x + \frac{5}{6}$

Combine the numerators over the common denominator.

$- 4 x + \frac{2 \cdot 2 + 7 \cdot 3}{6} = - 9 x + \frac{5}{6}$

Simplify the numerator.

Multiply $2$ by $2$ .

$- 4 x + \frac{4 + 7 \cdot 3}{6} = - 9 x + \frac{5}{6}$

Multiply $7$ by $3$ .

$- 4 x + \frac{4 + 21}{6} = - 9 x + \frac{5}{6}$

Add $4$ and $21$ .

$- 4 x + \frac{25}{6} = - 9 x + \frac{5}{6}$

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

Add $9 x$ to both sides of the equation.

$- 4 x + \frac{25}{6} + 9 x = \frac{5}{6}$

Add $- 4 x$ and $9 x$ .

$5 x + \frac{25}{6} = \frac{5}{6}$

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

Subtract $\frac{25}{6}$ from both sides of the equation.

$5 x = \frac{5}{6} - \frac{25}{6}$

Combine the numerators over the common denominator.

$5 x = \frac{5 - 25}{6}$

Subtract $25$ from $5$ .

$5 x = \frac{- 20}{6}$

Cancel the common factor of $- 20$ and $6$ .

Factor $2$ out of $- 20$ .

$5 x = \frac{2 (- 10)}{6}$

Cancel the common factors.

Factor $2$ out of $6$ .

$5 x = \frac{2 \cdot - 10}{2 \cdot 3}$

Cancel the common factor.

$5 x = \frac{2 \cdot - 10}{2 \cdot 3}$

Rewrite the expression.

$5 x = \frac{- 10}{3}$

Move the negative in front of the fraction.

$5 x = - \frac{10}{3}$

Divide each term in $5 x = - \frac{10}{3}$ by $5$ and simplify.

Divide each term in $5 x = - \frac{10}{3}$ by $5$ .

$\frac{5 x}{5} = \frac{- \frac{10}{3}}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{- \frac{10}{3}}{5}$

Divide $x$ by $1$ .

$x = \frac{- \frac{10}{3}}{5}$

Simplify the right side.

Multiply the numerator by the reciprocal of the denominator.

$x = - \frac{10}{3} \cdot \frac{1}{5}$

Cancel the common factor of $5$ .

Move the leading negative in $- \frac{10}{3}$ into the numerator.

$x = \frac{- 10}{3} \cdot \frac{1}{5}$

Factor $5$ out of $- 10$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Move the negative in front of the fraction.

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

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = - 0.\overline{6}$

Solve for x 2/3-4x+7/2=-9x+5/6

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