Solve for x 3/2+1/2x=2x

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

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

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

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

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

$\frac{3}{2} + \frac{x}{2} - 2 x = 0$

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

$\frac{3}{2} + \frac{x}{2} - 2 x \cdot \frac{2}{2} = 0$

Combine $- 2 x$ and $\frac{2}{2}$ .

$\frac{3}{2} + \frac{x}{2} + \frac{- 2 x \cdot 2}{2} = 0$

Combine the numerators over the common denominator.

$\frac{3}{2} + \frac{x - 2 x \cdot 2}{2} = 0$

Combine the numerators over the common denominator.

$\frac{3 + x - 2 x \cdot 2}{2} = 0$

Multiply $2$ by $- 2$ .

$\frac{3 + x - 4 x}{2} = 0$

Subtract $4 x$ from $x$ .

$\frac{3 - 3 x}{2} = 0$

Factor $3$ out of $3 - 3 x$ .

Factor $3$ out of $3$ .

$\frac{3 (1) - 3 x}{2} = 0$

Factor $3$ out of $- 3 x$ .

$\frac{3 (1) + 3 (- x)}{2} = 0$

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

$\frac{3 (1 - x)}{2} = 0$

Set the numerator equal to zero.

$3 (1 - x) = 0$

Solve the equation for $x$ .

Divide each term in $3 (1 - x) = 0$ by $3$ and simplify.

Divide each term in $3 (1 - x) = 0$ by $3$ .

$\frac{3 (1 - x)}{3} = \frac{0}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 (1 - x)}{3} = \frac{0}{3}$

Divide $1 - x$ by $1$ .

$1 - x = \frac{0}{3}$

Simplify the right side.

Divide $0$ by $3$ .

$1 - x = 0$

Subtract $1$ from both sides of the equation.

$- x = - 1$

Divide each term in $- x = - 1$ by $- 1$ and simplify.

Divide each term in $- x = - 1$ by $- 1$ .

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

Simplify the left side.

Dividing two negative values results in a positive value.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $- 1$ by $- 1$ .

$x = 1$

Solve for x 3/2+1/2x=2x

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