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

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

Step 1

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

Rewrite.

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

Simplify by adding zeros.

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

Apply the distributive property.

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

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

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

Multiply $\frac{2}{3} \cdot - 4$ .

Combine $\frac{2}{3}$ and $- 4$ .

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

Multiply $2$ by $- 4$ .

$\frac{2 x}{3} + \frac{- 8}{3} = 2 x$

Move the negative in front of the fraction.

$\frac{2 x}{3} - \frac{8}{3} = 2 x$

Step 2

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

Subtract $2 x$ from both sides of the equation.

$\frac{2 x}{3} - \frac{8}{3} - 2 x = 0$

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

$\frac{2 x}{3} - 2 x \cdot \frac{3}{3} - \frac{8}{3} = 0$

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

$\frac{2 x}{3} + \frac{- 2 x \cdot 3}{3} - \frac{8}{3} = 0$

Combine the numerators over the common denominator.

$\frac{2 x - 2 x \cdot 3}{3} - \frac{8}{3} = 0$

Combine the numerators over the common denominator.

$\frac{2 x - 2 x \cdot 3 - 8}{3} = 0$

Multiply $3$ by $- 2$ .

$\frac{2 x - 6 x - 8}{3} = 0$

Subtract $6 x$ from $2 x$ .

$\frac{- 4 x - 8}{3} = 0$

Factor $4$ out of $- 4 x - 8$ .

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

$\frac{4 (- x) - 8}{3} = 0$

Factor $4$ out of $- 8$ .

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

Factor $4$ out of $4 (- x) + 4 (- 2)$ .

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

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

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

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

$\frac{4 (- (x) - 1 (2))}{3} = 0$

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

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

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

$\frac{4 (- 1 (x + 2))}{3} = 0$

Move the negative in front of the fraction.

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

Step 3

Set the numerator equal to zero.

$4 (x + 2) = 0$

Step 4

Solve the equation for $x$ .

Divide each term in $4 (x + 2) = 0$ by $4$ and simplify.

Divide each term in $4 (x + 2) = 0$ by $4$ .

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

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

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

Divide $x + 2$ by $1$ .

$x + 2 = \frac{0}{4}$

Simplify the right side.

Divide $0$ by $4$ .

$x + 2 = 0$

Subtract $2$ from both sides of the equation.

$x = - 2$

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

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