Solve for x (x-4)/6-2=x/2

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

Step 1

Multiply both sides by $2$ .

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

Step 2

Simplify.

Simplify the left side.

Simplify $(\frac{x - 4}{6} - 2) \cdot 2$ .

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

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

Simplify terms.

Combine $- 2$ and $\frac{6}{6}$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $- 2$ by $6$ .

$\frac{x - 4 - 12}{6} \cdot 2 = \frac{x}{2} \cdot 2$

Subtract $12$ from $- 4$ .

$\frac{x - 16}{6} \cdot 2 = \frac{x}{2} \cdot 2$

Cancel the common factor of $2$ .

Factor $2$ out of $6$ .

$\frac{x - 16}{2 (3)} \cdot 2 = \frac{x}{2} \cdot 2$

Cancel the common factor.

$\frac{x - 16}{2 \cdot 3} \cdot 2 = \frac{x}{2} \cdot 2$

Rewrite the expression.

$\frac{x - 16}{3} = \frac{x}{2} \cdot 2$

Simplify the right side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{x - 16}{3} = \frac{x}{2} \cdot 2$

Rewrite the expression.

$\frac{x - 16}{3} = x$

Step 3

Solve for $x$ .

Multiply both sides by $3$ .

$\frac{x - 16}{3} \cdot 3 = x \cdot 3$

Simplify.

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{x - 16}{3} \cdot 3 = x \cdot 3$

Rewrite the expression.

$x - 16 = x \cdot 3$

Simplify the right side.

Move $3$ to the left of $x$ .

$x - 16 = 3 x$

Solve for $x$ .

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

Subtract $3 x$ from both sides of the equation.

$x - 16 - 3 x = 0$

Subtract $3 x$ from $x$ .

$- 2 x - 16 = 0$

Add $16$ to both sides of the equation.

$- 2 x = 16$

Divide each term in $- 2 x = 16$ by $- 2$ and simplify.

Divide each term in $- 2 x = 16$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{16}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{16}{- 2}$

Divide $x$ by $1$ .

$x = \frac{16}{- 2}$

Simplify the right side.

Divide $16$ by $- 2$ .

$x = - 8$

Solve for x (x-4)/6-2=x/2

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