Solve for x (x+2)/3-(x-2)/6=1/6

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

Step 1

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

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

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

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

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

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

Multiply $3$ by $2$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Apply the distributive property.

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

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

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

Multiply $2$ by $2$ .

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

Apply the distributive property.

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

Multiply $- 1$ by $- 2$ .

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

Subtract $x$ from $2 x$ .

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

Add $4$ and $2$ .

$\frac{x + 6}{6} = \frac{1}{6}$

Step 2

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$x + 6 = 1$

Step 3

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

Subtract $6$ from both sides of the equation.

$x = 1 - 6$

Subtract $6$ from $1$ .

$x = - 5$