Solve for x -x-1/2x=9

$- x - \frac{1}{2} x = 9$

Step 1

Simplify $- x - \frac{1}{2} x$ .

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

$- x - \frac{x}{2} = 9$

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

$- x \cdot \frac{2}{2} - \frac{x}{2} = 9$

Simplify terms.

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

$\frac{- x \cdot 2}{2} - \frac{x}{2} = 9$

Combine the numerators over the common denominator.

$\frac{- x \cdot 2 - x}{2} = 9$

Simplify the numerator.

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

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

$\frac{x (- 1 \cdot 2) - x}{2} = 9$

Factor $x$ out of $- x$ .

$\frac{x (- 1 \cdot 2) + x \cdot - 1}{2} = 9$

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

$\frac{x (- 1 \cdot 2 - 1)}{2} = 9$

Multiply $- 1$ by $2$ .

$\frac{x (- 2 - 1)}{2} = 9$

Subtract $1$ from $- 2$ .

$\frac{x \cdot - 3}{2} = 9$

Simplify the expression.

Move $- 3$ to the left of $x$ .

$\frac{- 3 \cdot x}{2} = 9$

Move the negative in front of the fraction.

$- \frac{3 x}{2} = 9$

Step 2

Multiply both sides of the equation by $- \frac{2}{3}$ .

$- \frac{2}{3} (- \frac{3 x}{2}) = - \frac{2}{3} \cdot 9$

Step 3

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{2}{3} (- \frac{3 x}{2})$ .

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{2}{3}$ into the numerator.

$\frac{- 2}{3} (- \frac{3 x}{2}) = - \frac{2}{3} \cdot 9$

Move the leading negative in $- \frac{3 x}{2}$ into the numerator.

$\frac{- 2}{3} \cdot \frac{- 3 x}{2} = - \frac{2}{3} \cdot 9$

Factor $2$ out of $- 2$ .

$\frac{2 (- 1)}{3} \cdot \frac{- 3 x}{2} = - \frac{2}{3} \cdot 9$

Cancel the common factor.

$\frac{2 \cdot - 1}{3} \cdot \frac{- 3 x}{2} = - \frac{2}{3} \cdot 9$

Rewrite the expression.

$\frac{- 1}{3} (- 3 x) = - \frac{2}{3} \cdot 9$

Cancel the common factor of $3$ .

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

$\frac{- 1}{3} (3 (- x)) = - \frac{2}{3} \cdot 9$

Cancel the common factor.

$\frac{- 1}{3} (3 (- x)) = - \frac{2}{3} \cdot 9$

Rewrite the expression.

$- - x = - \frac{2}{3} \cdot 9$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{2}{3} \cdot 9$

Multiply $x$ by $1$ .

$x = - \frac{2}{3} \cdot 9$

Simplify the right side.

Simplify $- \frac{2}{3} \cdot 9$ .

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{2}{3}$ into the numerator.

$x = \frac{- 2}{3} \cdot 9$

Factor $3$ out of $9$ .

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

Cancel the common factor.

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

Rewrite the expression.

$x = - 2 \cdot 3$

Multiply $- 2$ by $3$ .

$x = - 6$

Solve for x -x-1/2x=9

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