Solve for x 1/2x+1=3/2x-8

$\frac{1}{2} x + 1 = \frac{3}{2} x - 8$

Step 1

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

$\frac{x}{2} + 1 = \frac{3}{2} x - 8$

Step 2

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

$\frac{x}{2} + 1 = \frac{3 x}{2} - 8$

Step 3

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

Subtract $\frac{3 x}{2}$ from both sides of the equation.

$\frac{x}{2} + 1 - \frac{3 x}{2} = - 8$

Combine the numerators over the common denominator.

$1 + \frac{x - 3 x}{2} = - 8$

Subtract $3 x$ from $x$ .

$1 + \frac{- 2 x}{2} = - 8$

Cancel the common factor of $- 2$ and $2$ .

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

$1 + \frac{2 (- x)}{2} = - 8$

Cancel the common factors.

Factor $2$ out of $2$ .

$1 + \frac{2 (- x)}{2 (1)} = - 8$

Cancel the common factor.

$1 + \frac{2 (- x)}{2 \cdot 1} = - 8$

Rewrite the expression.

$1 + \frac{- x}{1} = - 8$

Divide $- x$ by $1$ .

$1 - x = - 8$

Step 4

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

Subtract $1$ from both sides of the equation.

$- x = - 8 - 1$

Subtract $1$ from $- 8$ .

$- x = - 9$

Step 5

Divide each term in $- x = - 9$ by $- 1$ and simplify.

Divide each term in $- x = - 9$ by $- 1$ .

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

Simplify the left side.

Dividing two negative values results in a positive value.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $- 9$ by $- 1$ .

$x = 9$