Solve for x 1/2(x-8)=3/2x+7

$\frac{1}{2} (x - 8) = \frac{3}{2} x + 7$

Step 1

Simplify $\frac{1}{2} \cdot (x - 8)$ .

Rewrite.

$0 + 0 + \frac{1}{2} \cdot (x - 8) = \frac{3}{2} x + 7$

Simplify by adding zeros.

$\frac{1}{2} \cdot (x - 8) = \frac{3}{2} x + 7$

Apply the distributive property.

$\frac{1}{2} x + \frac{1}{2} \cdot - 8 = \frac{3}{2} x + 7$

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

$\frac{x}{2} + \frac{1}{2} \cdot - 8 = \frac{3}{2} x + 7$

Cancel the common factor of $2$ .

Factor $2$ out of $- 8$ .

$\frac{x}{2} + \frac{1}{2} \cdot (2 (- 4)) = \frac{3}{2} x + 7$

Cancel the common factor.

$\frac{x}{2} + \frac{1}{2} \cdot (2 \cdot - 4) = \frac{3}{2} x + 7$

Rewrite the expression.

$\frac{x}{2} - 4 = \frac{3}{2} x + 7$

Step 2

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

$\frac{x}{2} - 4 = \frac{3 x}{2} + 7$

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.

$\frac{x}{2} - 4 - \frac{3 x}{2} = 7$

Combine the numerators over the common denominator.

$- 4 + \frac{x - 3 x}{2} = 7$

Subtract $3 x$ from $x$ .

$- 4 + \frac{- 2 x}{2} = 7$

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

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

$- 4 + \frac{2 (- x)}{2} = 7$

Cancel the common factors.

Factor $2$ out of $2$ .

$- 4 + \frac{2 (- x)}{2 (1)} = 7$

Cancel the common factor.

$- 4 + \frac{2 (- x)}{2 \cdot 1} = 7$

Rewrite the expression.

$- 4 + \frac{- x}{1} = 7$

Divide $- x$ by $1$ .

$- 4 - x = 7$

Step 4

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

Add $4$ to both sides of the equation.

$- x = 7 + 4$

Add $7$ and $4$ .

$- x = 11$

Step 5

Divide each term in $- x = 11$ by $- 1$ and simplify.

Divide each term in $- x = 11$ by $- 1$ .

$\frac{- x}{- 1} = \frac{11}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{11}{- 1}$

Divide $x$ by $1$ .

$x = \frac{11}{- 1}$

Simplify the right side.

Divide $11$ by $- 1$ .

$x = - 11$

Solve for x 1/2(x-8)=3/2x+7

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