Solve for w 2(12-w)=-2(w-17)-10

$2 (12 - w) = - 2 (w - 17) - 10$

Simplify $2 (12 - w)$ .

Rewrite.

$0 + 0 + 2 (12 - w) = - 2 (w - 17) - 10$

Simplify by adding zeros.

$2 (12 - w) = - 2 (w - 17) - 10$

Apply the distributive property.

$2 \cdot 12 + 2 (- w) = - 2 (w - 17) - 10$

Multiply.

Multiply $2$ by $12$ .

$24 + 2 (- w) = - 2 (w - 17) - 10$

Multiply $- 1$ by $2$ .

$24 - 2 w = - 2 (w - 17) - 10$

Simplify $- 2 (w - 17) - 10$ .

Simplify each term.

Apply the distributive property.

$24 - 2 w = - 2 w - 2 \cdot - 17 - 10$

Multiply $- 2$ by $- 17$ .

$24 - 2 w = - 2 w + 34 - 10$

Subtract $10$ from $34$ .

$24 - 2 w = - 2 w + 24$

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

Add $2 w$ to both sides of the equation.

$24 - 2 w + 2 w = 24$

Combine the opposite terms in $24 - 2 w + 2 w$ .

Add $- 2 w$ and $2 w$ .

$24 + 0 = 24$

Add $24$ and $0$ .

$24 = 24$

Since $24 = 24$ , the equation will always be true for any value of $w$ .

All real numbers

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$