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

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

Step 1

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

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

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

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{x + 2}{3}$ by $\frac{2}{2}$ .

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

Multiply $3$ by $2$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Apply the distributive property.

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

Move $2$ to the left of $x$ .

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

Multiply $2$ by $2$ .

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

Apply the distributive property.

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

Multiply $- 1$ by $2$ .

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

Multiply $- - x$ .

Multiply $- 1$ by $- 1$ .

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

Multiply $x$ by $1$ .

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

Add $2 x$ and $x$ .

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

Subtract $2$ from $4$ .

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

Step 2

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

Subtract $x$ from both sides of the equation.

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

To write $- x$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

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

Combine $- x$ and $\frac{6}{6}$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $6$ by $- 1$ .

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

Subtract $6 x$ from $3 x$ .

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

Factor $- 1$ out of $- 3 x$ .

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

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

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

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

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

Rewrite $- (3 x - 2)$ as $- 1 (3 x - 2)$ .

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

Move the negative in front of the fraction.

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

Step 3

Multiply both sides of the equation by $- 6$ .

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

Step 4

Simplify both sides of the equation.

Simplify the left side.

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

Cancel the common factor of $6$ .

Move the leading negative in $- \frac{3 x - 2}{6}$ into the numerator.

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

Factor $6$ out of $- 6$ .

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

Cancel the common factor.

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

Rewrite the expression.

$- - (3 x - 2) = - 6 \cdot - 2$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 (3 x - 2) = - 6 \cdot - 2$

Multiply $3 x - 2$ by $1$ .

$3 x - 2 = - 6 \cdot - 2$

Simplify the right side.

Multiply $- 6$ by $- 2$ .

$3 x - 2 = 12$

Step 5

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

Add $2$ to both sides of the equation.

$3 x = 12 + 2$

Add $12$ and $2$ .

$3 x = 14$

Step 6

Divide each term in $3 x = 14$ by $3$ and simplify.

Divide each term in $3 x = 14$ by $3$ .

$\frac{3 x}{3} = \frac{14}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{14}{3}$

Divide $x$ by $1$ .

$x = \frac{14}{3}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = \frac{14}{3}$

Decimal Form:

$x = 4.\overline{6}$

Mixed Number Form:

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

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

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