Solve for x (6x+2)/3-2=(4x-4)/6

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

Cancel the common factor of $4 x - 4$ and $6$ .

Factor $2$ out of $4 x$ .

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

Factor $2$ out of $- 4$ .

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

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

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

Cancel the common factors.

Factor $2$ out of $6$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{6 x + 2}{3} - 2 = \frac{2 x - 2}{3}$

Multiply both sides by $3$ .

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

Simplify.

Simplify the left side.

Simplify $(\frac{6 x + 2}{3} - 2) \cdot 3$ .

Factor $2$ out of $6 x + 2$ .

Factor $2$ out of $6 x$ .

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

Factor $2$ out of $2$ .

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

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

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

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

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

Simplify terms.

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

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

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

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

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

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

Multiply $- 1$ by $3$ .

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

Subtract $3$ from $1$ .

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

Simplify terms.

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

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

Apply the distributive property.

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

Multiply.

Multiply $3$ by $2$ .

$6 x + 2 \cdot - 2 = \frac{2 x - 2}{3} \cdot 3$

Multiply $2$ by $- 2$ .

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

Simplify the right side.

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

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

Factor $2$ out of $2 x$ .

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

Factor $2$ out of $- 2$ .

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

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

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

$6 x - 4 = 2 (x - 1)$

Apply the distributive property.

$6 x - 4 = 2 x + 2 \cdot - 1$

Multiply $2$ by $- 1$ .

$6 x - 4 = 2 x - 2$

Solve for $x$ .

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

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

$6 x - 4 - 2 x = - 2$

Subtract $2 x$ from $6 x$ .

$4 x - 4 = - 2$

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

Add $4$ to both sides of the equation.

$4 x = - 2 + 4$

Add $- 2$ and $4$ .

$4 x = 2$

Divide each term in $4 x = 2$ by $4$ and simplify.

Divide each term in $4 x = 2$ by $4$ .

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

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Cancel the common factor of $2$ and $4$ .

Factor $2$ out of $2$ .

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

Cancel the common factors.

Factor $2$ out of $4$ .

$x = \frac{2 \cdot 1}{2 \cdot 2}$

Cancel the common factor.

$x = \frac{2 \cdot 1}{2 \cdot 2}$

Rewrite the expression.

$x = \frac{1}{2}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1}{2}$

Decimal Form:

$x = 0.5$

Solve for x (6x+2)/3-2=(4x-4)/6

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