Solve for x -2(2-2x)-4(x+5)=-24

$- 2 (2 - 2 x) - 4 (x + 5) = - 24$

Step 1

Simplify $- 2 (2 - 2 x) - 4 (x + 5)$ .

Simplify each term.

Apply the distributive property.

$- 2 \cdot 2 - 2 (- 2 x) - 4 (x + 5) = - 24$

Multiply $- 2$ by $2$ .

$- 4 - 2 (- 2 x) - 4 (x + 5) = - 24$

Multiply $- 2$ by $- 2$ .

$- 4 + 4 x - 4 (x + 5) = - 24$

Apply the distributive property.

$- 4 + 4 x - 4 x - 4 \cdot 5 = - 24$

Multiply $- 4$ by $5$ .

$- 4 + 4 x - 4 x - 20 = - 24$

Simplify by adding terms.

Combine the opposite terms in $- 4 + 4 x - 4 x - 20$ .

Subtract $4 x$ from $4 x$ .

$- 4 + 0 - 20 = - 24$

Add $- 4$ and $0$ .

$- 4 - 20 = - 24$

Subtract $20$ from $- 4$ .

$- 24 = - 24$

Step 2

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

All real numbers

Step 3

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$