Solve for z -z/2+35=42

$- \frac{z}{2} + 35 = 42$

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

Subtract $35$ from both sides of the equation.

$- \frac{z}{2} = 42 - 35$

Subtract $35$ from $42$ .

$- \frac{z}{2} = 7$

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

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

Simplify both sides of the equation.

Simplify the left side.

Simplify $- 2 (- \frac{z}{2})$ .

Cancel the common factor of $2$ .

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

$- 2 \frac{- z}{2} = - 2 \cdot 7$

Factor $2$ out of $- 2$ .

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

Cancel the common factor.

$2 \cdot - 1 \frac{- z}{2} = - 2 \cdot 7$

Rewrite the expression.

$- - z = - 2 \cdot 7$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 z = - 2 \cdot 7$

Multiply $z$ by $1$ .

$z = - 2 \cdot 7$

Simplify the right side.

Multiply $- 2$ by $7$ .

$z = - 14$