Solve for g 1/2*(3g-2)=g/2

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

Step 1

Multiply both sides by $2$ .

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

Step 2

Simplify.

Simplify the left side.

Simplify $\frac{1}{2} \cdot (3 g - 2) \cdot 2$ .

Apply the distributive property.

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

Multiply $\frac{1}{2} (3 g)$ .

Combine $3$ and $\frac{1}{2}$ .

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

Combine $\frac{3}{2}$ and $g$ .

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

Cancel the common factor of $2$ .

Factor $2$ out of $- 2$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Apply the distributive property.

$\frac{3 g}{2} \cdot 2 - 1 \cdot 2 = \frac{g}{2} \cdot 2$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{3 g}{2} \cdot 2 - 1 \cdot 2 = \frac{g}{2} \cdot 2$

Rewrite the expression.

$3 g - 1 \cdot 2 = \frac{g}{2} \cdot 2$

Multiply $- 1$ by $2$ .

$3 g - 2 = \frac{g}{2} \cdot 2$

Simplify the right side.

Cancel the common factor of $2$ .

Cancel the common factor.

$3 g - 2 = \frac{g}{2} \cdot 2$

Rewrite the expression.

$3 g - 2 = g$

Step 3

Solve for $g$ .

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

Subtract $g$ from both sides of the equation.

$3 g - 2 - g = 0$

Subtract $g$ from $3 g$ .

$2 g - 2 = 0$

Add $2$ to both sides of the equation.

$2 g = 2$

Divide each term in $2 g = 2$ by $2$ and simplify.

Divide each term in $2 g = 2$ by $2$ .

$\frac{2 g}{2} = \frac{2}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 g}{2} = \frac{2}{2}$

Divide $g$ by $1$ .

$g = \frac{2}{2}$

Simplify the right side.

Divide $2$ by $2$ .

$g = 1$

Solve for g 1/2*(3g-2)=g/2

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