Solve for x (x-2)/2+(x-2(x-4))/6=x/3

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

Step 1

Multiply both sides by $3$ .

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

Step 2

Simplify.

Simplify the left side.

Simplify $(\frac{x - 2}{2} + \frac{x - 2 (x - 4)}{6}) \cdot 3$ .

Simplify the numerator.

Apply the distributive property.

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

Multiply $- 2$ by $- 4$ .

$(\frac{x - 2}{2} + \frac{x - 2 x + 8}{6}) \cdot 3 = \frac{x}{3} \cdot 3$

Subtract $2 x$ from $x$ .

$(\frac{x - 2}{2} + \frac{- x + 8}{6}) \cdot 3 = \frac{x}{3} \cdot 3$

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

$(\frac{x - 2}{2} \cdot \frac{3}{3} + \frac{- x + 8}{6}) \cdot 3 = \frac{x}{3} \cdot 3$

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

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

$(\frac{(x - 2) \cdot 3}{2 \cdot 3} + \frac{- x + 8}{6}) \cdot 3 = \frac{x}{3} \cdot 3$

Multiply $2$ by $3$ .

$(\frac{(x - 2) \cdot 3}{6} + \frac{- x + 8}{6}) \cdot 3 = \frac{x}{3} \cdot 3$

Combine the numerators over the common denominator.

$\frac{(x - 2) \cdot 3 - x + 8}{6} \cdot 3 = \frac{x}{3} \cdot 3$

Simplify the numerator.

Apply the distributive property.

$\frac{x \cdot 3 - 2 \cdot 3 - x + 8}{6} \cdot 3 = \frac{x}{3} \cdot 3$

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

$\frac{3 \cdot x - 2 \cdot 3 - x + 8}{6} \cdot 3 = \frac{x}{3} \cdot 3$

Multiply $- 2$ by $3$ .

$\frac{3 \cdot x - 6 - x + 8}{6} \cdot 3 = \frac{x}{3} \cdot 3$

Subtract $x$ from $3 x$ .

$\frac{2 x - 6 + 8}{6} \cdot 3 = \frac{x}{3} \cdot 3$

Add $- 6$ and $8$ .

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

Factor $2$ out of $2 x + 2$ .

Factor $2$ out of $2 x$ .

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

Factor $2$ out of $2$ .

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

Factor $2$ out of $2 (x) + 2 (1)$ .

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

Reduce the expression by cancelling the common factors.

Cancel the common factor of $3$ .

Factor $3$ out of $6$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $x + 1$ by $1$ .

$x + 1 = \frac{x}{3} \cdot 3$

Simplify the right side.

Cancel the common factor of $3$ .

Cancel the common factor.

$x + 1 = \frac{x}{3} \cdot 3$

Rewrite the expression.

$x + 1 = x$

Step 3

Solve for $x$ .

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

Subtract $x$ from both sides of the equation.

$x + 1 - x = 0$

Combine the opposite terms in $x + 1 - x$ .

Subtract $x$ from $x$ .

$0 + 1 = 0$

Add $0$ and $1$ .

$1 = 0$

Since $1 \neq 0$ , there are no solutions.

No solution

Solve for x (x-2)/2+(x-2(x-4))/6=x/3

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