Solve for x 2/7(x-2)=4x

$\frac{2}{7} (x - 2) = 4 x$

Step 1

Simplify $\frac{2}{7} \cdot (x - 2)$ .

Start simplifying.

$0 + 0 + \frac{2}{7} \cdot (x - 2) = 4 x$

Simplify by adding zeros.

$\frac{2}{7} \cdot (x - 2) = 4 x$

Apply the distributive property.

$\frac{2}{7} x + \frac{2}{7} \cdot - 2 = 4 x$

Combine $\frac{2}{7}$ and $x$ .

$\frac{2 x}{7} + \frac{2}{7} \cdot - 2 = 4 x$

Multiply $\frac{2}{7} \cdot - 2$ .

Combine $\frac{2}{7}$ and $- 2$ .

$\frac{2 x}{7} + \frac{2 \cdot - 2}{7} = 4 x$

Multiply $2$ by $- 2$ .

$\frac{2 x}{7} + \frac{- 4}{7} = 4 x$

Move the negative in front of the fraction.

$\frac{2 x}{7} - \frac{4}{7} = 4 x$

Step 2

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

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

$\frac{2 x}{7} - \frac{4}{7} - 4 x = 0$

To write $- 4 x$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{2 x}{7} - 4 x \cdot \frac{7}{7} - \frac{4}{7} = 0$

Combine $- 4 x$ and $\frac{7}{7}$ .

$\frac{2 x}{7} + \frac{- 4 x \cdot 7}{7} - \frac{4}{7} = 0$

Combine the numerators over the common denominator.

$\frac{2 x - 4 x \cdot 7}{7} - \frac{4}{7} = 0$

Combine the numerators over the common denominator.

$\frac{2 x - 4 x \cdot 7 - 4}{7} = 0$

Multiply $7$ by $- 4$ .

$\frac{2 x - 28 x - 4}{7} = 0$

Subtract $28 x$ from $2 x$ .

$\frac{- 26 x - 4}{7} = 0$

Factor $2$ out of $- 26 x - 4$ .

Factor $2$ out of $- 26 x$ .

$\frac{2 (- 13 x) - 4}{7} = 0$

Factor $2$ out of $- 4$ .

$\frac{2 (- 13 x) + 2 (- 2)}{7} = 0$

Factor $2$ out of $2 (- 13 x) + 2 (- 2)$ .

$\frac{2 (- 13 x - 2)}{7} = 0$

Factor $- 1$ out of $- 13 x$ .

$\frac{2 (- (13 x) - 2)}{7} = 0$

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

$\frac{2 (- (13 x) - 1 (2))}{7} = 0$

Factor $- 1$ out of $- (13 x) - 1 (2)$ .

$\frac{2 (- (13 x + 2))}{7} = 0$

Rewrite $- (13 x + 2)$ as $- 1 (13 x + 2)$ .

$\frac{2 (- 1 (13 x + 2))}{7} = 0$

Move the negative in front of the fraction.

$- \frac{2 (13 x + 2)}{7} = 0$

Step 3

Set the numerator equal to zero.

$2 (13 x + 2) = 0$

Step 4

Solve the equation for $x$ .

Divide each term in $2 (13 x + 2) = 0$ by $2$ and simplify.

Divide each term in $2 (13 x + 2) = 0$ by $2$ .

$\frac{2 (13 x + 2)}{2} = \frac{0}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 (13 x + 2)}{2} = \frac{0}{2}$

Divide $13 x + 2$ by $1$ .

$13 x + 2 = \frac{0}{2}$

Simplify the right side.

Divide $0$ by $2$ .

$13 x + 2 = 0$

Subtract $2$ from both sides of the equation.

$13 x = - 2$

Divide each term in $13 x = - 2$ by $13$ and simplify.

Divide each term in $13 x = - 2$ by $13$ .

$\frac{13 x}{13} = \frac{- 2}{13}$

Simplify the left side.

Cancel the common factor of $13$ .

Cancel the common factor.

$\frac{13 x}{13} = \frac{- 2}{13}$

Divide $x$ by $1$ .

$x = \frac{- 2}{13}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{2}{13}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{2}{13}$

Decimal Form:

$x = - 0.\overline{153846}$

Solve for x 2/7(x-2)=4x

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