Solve for x 1/2(x-10)=7

$\frac{1}{2} (x - 10) = 7$

Step 1

Multiply both sides of the equation by $2$ .

$2 (\frac{1}{2} \cdot (x - 10)) = 2 \cdot 7$

Step 2

Simplify both sides of the equation.

Simplify the left side.

Simplify $2 (\frac{1}{2} \cdot (x - 10))$ .

Apply the distributive property.

$2 (\frac{1}{2} x + \frac{1}{2} \cdot - 10) = 2 \cdot 7$

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

$2 (\frac{x}{2} + \frac{1}{2} \cdot - 10) = 2 \cdot 7$

Cancel the common factor of $2$ .

Factor $2$ out of $- 10$ .

$2 (\frac{x}{2} + \frac{1}{2} \cdot (2 (- 5))) = 2 \cdot 7$

Cancel the common factor.

$2 (\frac{x}{2} + \frac{1}{2} \cdot (2 \cdot - 5)) = 2 \cdot 7$

Rewrite the expression.

$2 (\frac{x}{2} - 5) = 2 \cdot 7$

Apply the distributive property.

$2 \frac{x}{2} + 2 \cdot - 5 = 2 \cdot 7$

Cancel the common factor of $2$ .

Cancel the common factor.

$2 \frac{x}{2} + 2 \cdot - 5 = 2 \cdot 7$

Rewrite the expression.

$x + 2 \cdot - 5 = 2 \cdot 7$

Multiply $2$ by $- 5$ .

$x - 10 = 2 \cdot 7$

Simplify the right side.

Multiply $2$ by $7$ .

$x - 10 = 14$

Step 3

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

Add $10$ to both sides of the equation.

$x = 14 + 10$

Add $14$ and $10$ .

$x = 24$