Solve for x (x-2)/3+1/6=5/6

$\frac{x - 2}{3} + \frac{1}{6} = \frac{5}{6}$

Step 1

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

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

$\frac{x - 2}{3} \cdot \frac{2}{2} + \frac{1}{6} = \frac{5}{6}$

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

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

$\frac{(x - 2) \cdot 2}{3 \cdot 2} + \frac{1}{6} = \frac{5}{6}$

Multiply $3$ by $2$ .

$\frac{(x - 2) \cdot 2}{6} + \frac{1}{6} = \frac{5}{6}$

Combine the numerators over the common denominator.

$\frac{(x - 2) \cdot 2 + 1}{6} = \frac{5}{6}$

Simplify the numerator.

Apply the distributive property.

$\frac{x \cdot 2 - 2 \cdot 2 + 1}{6} = \frac{5}{6}$

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

$\frac{2 \cdot x - 2 \cdot 2 + 1}{6} = \frac{5}{6}$

Multiply $- 2$ by $2$ .

$\frac{2 \cdot x - 4 + 1}{6} = \frac{5}{6}$

Add $- 4$ and $1$ .

$\frac{2 x - 3}{6} = \frac{5}{6}$

Step 2

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

$2 x - 3 = 5$

Step 3

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

Add $3$ to both sides of the equation.

$2 x = 5 + 3$

Add $5$ and $3$ .

$2 x = 8$

Step 4

Divide each term in $2 x = 8$ by $2$ and simplify.

Divide each term in $2 x = 8$ by $2$ .

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $8$ by $2$ .

$x = 4$