Solve for x 3x+1=(4x-2)/2

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

Step 1

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

Factor $2$ out of $4 x$ .

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

Factor $2$ out of $- 2$ .

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

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

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

Cancel the common factors.

Factor $2$ out of $2$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Divide $2 x - 1$ by $1$ .

$3 x + 1 = 2 x - 1$

Step 2

Solve for $x$ .

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

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

$3 x + 1 - 2 x = - 1$

Subtract $2 x$ from $3 x$ .

$x + 1 = - 1$

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

Subtract $1$ from both sides of the equation.

$x = - 1 - 1$

Subtract $1$ from $- 1$ .

$x = - 2$