Solve for x 12-1/2(x-8)=15

$12 - \frac{1}{2} (x - 8) = 15$

Step 1

Simplify $12 - \frac{1}{2} \cdot (x - 8)$ .

Simplify each term.

Apply the distributive property.

$12 - \frac{1}{2} x - \frac{1}{2} \cdot - 8 = 15$

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

$12 - \frac{x}{2} - \frac{1}{2} \cdot - 8 = 15$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$12 - \frac{x}{2} + \frac{- 1}{2} \cdot - 8 = 15$

Factor $2$ out of $- 8$ .

$12 - \frac{x}{2} + \frac{- 1}{2} \cdot (2 (- 4)) = 15$

Cancel the common factor.

$12 - \frac{x}{2} + \frac{- 1}{2} \cdot (2 \cdot - 4) = 15$

Rewrite the expression.

$12 - \frac{x}{2} - 1 \cdot - 4 = 15$

Multiply $- 1$ by $- 4$ .

$12 - \frac{x}{2} + 4 = 15$

Add $12$ and $4$ .

$- \frac{x}{2} + 16 = 15$

Step 2

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

Subtract $16$ from both sides of the equation.

$- \frac{x}{2} = 15 - 16$

Subtract $16$ from $15$ .

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

Step 3

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

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

Step 4

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 12-1/2(x-8)=15

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