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

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

Simplify $x + \frac{x}{2}$ .

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

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

Simplify terms.

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

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

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

Add $2 x$ and $x$ .

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

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

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

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

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

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

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Factor $x$ out of $3 x - 2 x \cdot 2$ .

Factor $x$ out of $3 x$ .

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

Factor $x$ out of $- 2 x \cdot 2$ .

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

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

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

Multiply $- 2$ by $2$ .

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

Subtract $4$ from $3$ .

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

Move $- 1$ to the left of $x$ .

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

Move the negative in front of the fraction.

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

Multiply both sides of the equation by $- 2$ .

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

Simplify both sides of the equation.

Simplify the left side.

Simplify $- 2 (- \frac{x}{2})$ .

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{x}{2}$ into the numerator.

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

Factor $2$ out of $- 2$ .

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

Cancel the common factor.

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

Rewrite the expression.

$- - x = - 2 \cdot 1$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 x = - 2 \cdot 1$

Multiply $x$ by $1$ .

$x = - 2 \cdot 1$

Simplify the right side.

Multiply $- 2$ by $1$ .

$x = - 2$

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

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