Solve for x -9=-3/2x+3

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

Step 1

Rewrite the equation as $- \frac{3}{2} x + 3 = - 9$ .

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

Step 2

Simplify each term.

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

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

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

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

Step 3

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

Subtract $3$ from both sides of the equation.

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

Subtract $3$ from $- 9$ .

$- \frac{3 x}{2} = - 12$

Step 4

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

$- \frac{2}{3} (- \frac{3 x}{2}) = - \frac{2}{3} \cdot - 12$

Step 5

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.

$\frac{- 2}{3} (- \frac{3 x}{2}) = - \frac{2}{3} \cdot - 12$

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

$\frac{- 2}{3} \cdot \frac{- 3 x}{2} = - \frac{2}{3} \cdot - 12$

Factor $2$ out of $- 2$ .

$\frac{2 (- 1)}{3} \cdot \frac{- 3 x}{2} = - \frac{2}{3} \cdot - 12$

Cancel the common factor.

$\frac{2 \cdot - 1}{3} \cdot \frac{- 3 x}{2} = - \frac{2}{3} \cdot - 12$

Rewrite the expression.

$\frac{- 1}{3} (- 3 x) = - \frac{2}{3} \cdot - 12$

Cancel the common factor of $3$ .

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

$\frac{- 1}{3} (3 (- x)) = - \frac{2}{3} \cdot - 12$

Cancel the common factor.

$\frac{- 1}{3} (3 (- x)) = - \frac{2}{3} \cdot - 12$

Rewrite the expression.

$- - x = - \frac{2}{3} \cdot - 12$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{2}{3} \cdot - 12$

Multiply $x$ by $1$ .

$x = - \frac{2}{3} \cdot - 12$

Simplify the right side.

Simplify $- \frac{2}{3} \cdot - 12$ .

Cancel the common factor of $3$ .

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

$x = \frac{- 2}{3} \cdot - 12$

Factor $3$ out of $- 12$ .

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

Cancel the common factor.

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

Rewrite the expression.

$x = - 2 \cdot - 4$

Multiply $- 2$ by $- 4$ .

$x = 8$

Solve for x -9=-3/2x+3

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