Solve for x (2x-3)/6=(2x)/3+1/2

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

Step 1

Multiply both sides by $6$ .

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

Step 2

Simplify.

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify the right side.

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

Apply the distributive property.

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

Cancel the common factor of $3$ .

Factor $3$ out of $6$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $2$ by $2$ .

$2 x - 3 = 4 x + \frac{1}{2} \cdot 6$

Cancel the common factor of $2$ .

Factor $2$ out of $6$ .

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

Cancel the common factor.

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

Rewrite the expression.

$2 x - 3 = 4 x + 3$

Step 3

Solve for $x$ .

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

Subtract $4 x$ from both sides of the equation.

$2 x - 3 - 4 x = 3$

Subtract $4 x$ from $2 x$ .

$- 2 x - 3 = 3$

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

Add $3$ to both sides of the equation.

$- 2 x = 3 + 3$

Add $3$ and $3$ .

$- 2 x = 6$

Divide each term in $- 2 x = 6$ by $- 2$ and simplify.

Divide each term in $- 2 x = 6$ by $- 2$ .

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

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $6$ by $- 2$ .

$x = - 3$

Solve for x (2x-3)/6=(2x)/3+1/2

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