Solve for x 2/3-2x=5+4/3x

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

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

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

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

Subtract $\frac{4 x}{3}$ from both sides of the equation.

$\frac{2}{3} - 2 x - \frac{4 x}{3} = 5$

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

$\frac{2}{3} - 2 x \cdot \frac{3}{3} - \frac{4 x}{3} = 5$

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

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

Combine the numerators over the common denominator.

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

Combine the numerators over the common denominator.

$\frac{2 - 2 x \cdot 3 - 4 x}{3} = 5$

Multiply $3$ by $- 2$ .

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

Subtract $4 x$ from $- 6 x$ .

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

Factor $2$ out of $2 - 10 x$ .

Factor $2$ out of $2$ .

$\frac{2 (1) - 10 x}{3} = 5$

Factor $2$ out of $- 10 x$ .

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

Factor $2$ out of $2 (1) + 2 (- 5 x)$ .

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

Multiply both sides by $3$ .

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

Simplify.

Simplify the left side.

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

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

Apply the distributive property.

$2 \cdot 1 + 2 (- 5 x) = 5 \cdot 3$

Simplify the expression.

Multiply $2$ by $1$ .

$2 + 2 (- 5 x) = 5 \cdot 3$

Multiply $- 5$ by $2$ .

$2 - 10 x = 5 \cdot 3$

Reorder $2$ and $- 10 x$ .

$- 10 x + 2 = 5 \cdot 3$

Simplify the right side.

Multiply $5$ by $3$ .

$- 10 x + 2 = 15$

Solve for $x$ .

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

Subtract $2$ from both sides of the equation.

$- 10 x = 15 - 2$

Subtract $2$ from $15$ .

$- 10 x = 13$

Divide each term in $- 10 x = 13$ by $- 10$ and simplify.

Divide each term in $- 10 x = 13$ by $- 10$ .

$\frac{- 10 x}{- 10} = \frac{13}{- 10}$

Simplify the left side.

Cancel the common factor of $- 10$ .

Cancel the common factor.

$\frac{- 10 x}{- 10} = \frac{13}{- 10}$

Divide $x$ by $1$ .

$x = \frac{13}{- 10}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{13}{10}$

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{13}{10}$

Decimal Form:

$x = - 1.3$

Mixed Number Form:

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

Solve for x 2/3-2x=5+4/3x

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