Solve for x (3x-2)/12-1/6=1/6

$\frac{3 x - 2}{12} - \frac{1}{6} = \frac{1}{6}$

Step 1

Simplify $\frac{3 x - 2}{12} - \frac{1}{6}$ .

To write $- \frac{1}{6}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{3 x - 2}{12} - \frac{1}{6} \cdot \frac{2}{2} = \frac{1}{6}$

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{6}$ by $\frac{2}{2}$ .

$\frac{3 x - 2}{12} - \frac{2}{6 \cdot 2} = \frac{1}{6}$

Multiply $6$ by $2$ .

$\frac{3 x - 2}{12} - \frac{2}{12} = \frac{1}{6}$

Combine the numerators over the common denominator.

$\frac{3 x - 2 - 2}{12} = \frac{1}{6}$

Subtract $2$ from $- 2$ .

$\frac{3 x - 4}{12} = \frac{1}{6}$

Step 2

Multiply both sides by $12$ .

$\frac{3 x - 4}{12} \cdot 12 = \frac{1}{6} \cdot 12$

Step 3

Simplify.

Simplify the left side.

Cancel the common factor of $12$ .

Cancel the common factor.

$\frac{3 x - 4}{12} \cdot 12 = \frac{1}{6} \cdot 12$

Rewrite the expression.

$3 x - 4 = \frac{1}{6} \cdot 12$

Simplify the right side.

Cancel the common factor of $6$ .

Factor $6$ out of $12$ .

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

Cancel the common factor.

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

Rewrite the expression.

$3 x - 4 = 2$

Step 4

Solve for $x$ .

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

Add $4$ to both sides of the equation.

$3 x = 2 + 4$

Add $2$ and $4$ .

$3 x = 6$

Divide each term in $3 x = 6$ by $3$ and simplify.

Divide each term in $3 x = 6$ by $3$ .

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

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $6$ by $3$ .

$x = 2$

Solve for x (3x-2)/12-1/6=1/6

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