Solve for x 5/6=-2/5x-2/3

$\frac{5}{6} = - \frac{2}{5} x - \frac{2}{3}$

Rewrite the equation as $- \frac{2}{5} x - \frac{2}{3} = \frac{5}{6}$ .

$- \frac{2}{5} x - \frac{2}{3} = \frac{5}{6}$

Simplify each term.

Combine $x$ and $\frac{2}{5}$ .

$- \frac{x \cdot 2}{5} - \frac{2}{3} = \frac{5}{6}$

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

$- \frac{2 x}{5} - \frac{2}{3} = \frac{5}{6}$

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

Add $\frac{2}{3}$ to both sides of the equation.

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

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

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

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

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

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

Multiply $3$ by $2$ .

$- \frac{2 x}{5} = \frac{5}{6} + \frac{2 \cdot 2}{6}$

Combine the numerators over the common denominator.

$- \frac{2 x}{5} = \frac{5 + 2 \cdot 2}{6}$

Simplify the numerator.

Multiply $2$ by $2$ .

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

Add $5$ and $4$ .

$- \frac{2 x}{5} = \frac{9}{6}$

Cancel the common factor of $9$ and $6$ .

Factor $3$ out of $9$ .

$- \frac{2 x}{5} = \frac{3 (3)}{6}$

Cancel the common factors.

Factor $3$ out of $6$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply both sides of the equation by $- \frac{5}{2}$ .

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

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{5}{2} (- \frac{2 x}{5})$ .

Cancel the common factor of $5$ .

Move the leading negative in $- \frac{5}{2}$ into the numerator.

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

Move the leading negative in $- \frac{2 x}{5}$ into the numerator.

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

Factor $5$ out of $- 5$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $2$ .

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply.

Multiply $- 1$ by $- 1$ .

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

Multiply $x$ by $1$ .

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

Simplify the right side.

Multiply $- \frac{5}{2} \cdot \frac{3}{2}$ .

Multiply $\frac{3}{2}$ by $\frac{5}{2}$ .

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

Multiply $3$ by $5$ .

$x = - \frac{15}{2 \cdot 2}$

Multiply $2$ by $2$ .

$x = - \frac{15}{4}$

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{15}{4}$

Decimal Form:

$x = - 3.75$

Mixed Number Form:

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

Solve for x 5/6=-2/5x-2/3

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