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

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

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

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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 $1$ .

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

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

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.

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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 $1$ .

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

Reduce the expression by cancelling the common factors.

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Split the fraction into multiple fractions.

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

Reduce the expression $\frac{2 x}{6}$ by cancelling the common factors.

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Factor $2$ out of $2 x$ .

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

Factor $2$ out of $6$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Reduce the expression $\frac{3}{6}$ by cancelling the common factors.

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Factor $3$ out of $3$ .

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

Factor $3$ out of $6$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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Add $\frac{1}{2}$ to both sides of the equation.

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

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

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

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Multiply $\frac{1}{2}$ and $\frac{3}{3}$ .

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

Multiply $2$ by $3$ .

$\frac{x}{3} = \frac{5}{6} + \frac{3}{6}$

Combine the numerators over the common denominator.

$\frac{x}{3} = \frac{5 + 3}{6}$

Add $5$ and $3$ .

$\frac{x}{3} = \frac{8}{6}$

Cancel the common factor of $8$ and $6$ .

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Factor $2$ out of $8$ .

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

Cancel the common factors.

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Factor $2$ out of $6$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

$x = 4$

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

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