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

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

Step 1

Cancel the common factor of $6 x - 2$ and $4$ .

Factor $2$ out of $6 x$ .

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

Factor $2$ out of $- 2$ .

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

Factor $2$ out of $2 (3 x) + 2 (- 1)$ .

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

Cancel the common factors.

Factor $2$ out of $4$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 2

Multiply both sides by $2$ .

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

Step 3

Simplify.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$3 x - 1 = (x - 2) \cdot 2$

Simplify the right side.

Simplify $(x - 2) \cdot 2$ .

Apply the distributive property.

$3 x - 1 = x \cdot 2 - 2 \cdot 2$

Simplify the expression.

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

$3 x - 1 = 2 \cdot x - 2 \cdot 2$

Multiply $- 2$ by $2$ .

$3 x - 1 = 2 x - 4$

Step 4

Solve for $x$ .

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

Subtract $2 x$ from both sides of the equation.

$3 x - 1 - 2 x = - 4$

Subtract $2 x$ from $3 x$ .

$x - 1 = - 4$

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

Add $1$ to both sides of the equation.

$x = - 4 + 1$

Add $- 4$ and $1$ .

$x = - 3$

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

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