Solve for x 2/3(x-2)=4x

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

Step 1

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

Start simplifying.

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

Simplify by adding zeros.

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

Apply the distributive property.

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

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

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

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

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

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

Multiply $2$ by $- 2$ .

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

Move the negative in front of the fraction.

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

Step 2

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

Subtract $4 x$ from both sides of the equation.

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

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

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

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

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

Combine the numerators over the common denominator.

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

Combine the numerators over the common denominator.

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

Multiply $3$ by $- 4$ .

$\frac{2 x - 12 x - 4}{3} = 0$

Subtract $12 x$ from $2 x$ .

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

Factor $2$ out of $- 10 x - 4$ .

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

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

Factor $2$ out of $- 4$ .

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

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

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

Factor $- 1$ out of $- 5 x$ .

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

Rewrite $- 2$ as $- 1 (2)$ .

$\frac{2 (- (5 x) - 1 (2))}{3} = 0$

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

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

Rewrite $- (5 x + 2)$ as $- 1 (5 x + 2)$ .

$\frac{2 (- 1 (5 x + 2))}{3} = 0$

Move the negative in front of the fraction.

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

Step 3

Set the numerator equal to zero.

$2 (5 x + 2) = 0$

Step 4

Solve the equation for $x$ .

Divide each term in $2 (5 x + 2) = 0$ by $2$ and simplify.

Divide each term in $2 (5 x + 2) = 0$ by $2$ .

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $5 x + 2$ by $1$ .

$5 x + 2 = \frac{0}{2}$

Simplify the right side.

Divide $0$ by $2$ .

$5 x + 2 = 0$

Subtract $2$ from both sides of the equation.

$5 x = - 2$

Divide each term in $5 x = - 2$ by $5$ and simplify.

Divide each term in $5 x = - 2$ by $5$ .

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

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Move the negative in front of the fraction.

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = - 0.4$

Solve for x 2/3(x-2)=4x

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