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

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

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

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

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

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

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

To write $- 4 x$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Simplify terms.

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

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

Combine the numerators over the common denominator.

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

Simplify each term.

Simplify the numerator.

Factor $2 x$ out of $2 x - 4 x \cdot 3$ .

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

$\frac{2 x (1) - 4 x \cdot 3}{3} + 2 = - 4 x$

Factor $2 x$ out of $- 4 x \cdot 3$ .

$\frac{2 x (1) + 2 x (- 2 \cdot 3)}{3} + 2 = - 4 x$

Factor $2 x$ out of $2 x (1) + 2 x (- 2 \cdot 3)$ .

$\frac{2 x (1 - 2 \cdot 3)}{3} + 2 = - 4 x$

Multiply $- 2$ by $3$ .

$\frac{2 x (1 - 6)}{3} + 2 = - 4 x$

Subtract $6$ from $1$ .

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

Multiply $- 5$ by $2$ .

$\frac{- 10 x}{3} + 2 = - 4 x$

Move the negative in front of the fraction.

$- \frac{10 x}{3} + 2 = - 4 x$

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

Add $4 x$ to both sides of the equation.

$- \frac{10 x}{3} + 2 + 4 x = 0$

To write $4 x$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{10 x}{3} + 4 x \cdot \frac{3}{3} + 2 = 0$

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

$- \frac{10 x}{3} + \frac{4 x \cdot 3}{3} + 2 = 0$

Combine the numerators over the common denominator.

$\frac{- 10 x + 4 x \cdot 3}{3} + 2 = 0$

Simplify the numerator.

Factor $2 x$ out of $- 10 x + 4 x \cdot 3$ .

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

$\frac{2 x (- 5) + 4 x \cdot 3}{3} + 2 = 0$

Factor $2 x$ out of $4 x \cdot 3$ .

$\frac{2 x (- 5) + 2 x (2 \cdot 3)}{3} + 2 = 0$

Factor $2 x$ out of $2 x (- 5) + 2 x (2 \cdot 3)$ .

$\frac{2 x (- 5 + 2 \cdot 3)}{3} + 2 = 0$

Multiply $2$ by $3$ .

$\frac{2 x (- 5 + 6)}{3} + 2 = 0$

Add $- 5$ and $6$ .

$\frac{2 x \cdot 1}{3} + 2 = 0$

Multiply $2$ by $1$ .

$\frac{2 x}{3} + 2 = 0$

Subtract $2$ from both sides of the equation.

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

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

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

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{3}{2} \cdot \frac{2 x}{3}$ .

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $2$ .

Factor $2$ out of $2 x$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Simplify the right side.

Simplify $\frac{3}{2} \cdot - 2$ .

Cancel the common factor of $2$ .

Factor $2$ out of $- 2$ .

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

Cancel the common factor.

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

Rewrite the expression.

$x = 3 \cdot - 1$

Multiply $3$ by $- 1$ .

$x = - 3$

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

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