Solve for x 4-(2x+5)=1/2(-4x-2)

$4 - (2 x + 5) = \frac{1}{2} (- 4 x - 2)$

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

Simplify each term.

Apply the distributive property.

$4 - (2 x) - 1 \cdot 5 = \frac{1}{2} \cdot (- 4 x - 2)$

Multiply $2$ by $- 1$ .

$4 - 2 x - 1 \cdot 5 = \frac{1}{2} \cdot (- 4 x - 2)$

Multiply $- 1$ by $5$ .

$4 - 2 x - 5 = \frac{1}{2} \cdot (- 4 x - 2)$

Subtract $5$ from $4$ .

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

Simplify $\frac{1}{2} \cdot (- 4 x - 2)$ .

Apply the distributive property.

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

Cancel the common factor of $2$ .

Factor $2$ out of $- 4 x$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $2$ .

Factor $2$ out of $- 2$ .

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

Cancel the common factor.

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

Rewrite the expression.

$- 2 x - 1 = - 2 x - 1$

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

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

$- 2 x - 1 + 2 x = - 1$

Combine the opposite terms in $- 2 x - 1 + 2 x$ .

Add $- 2 x$ and $2 x$ .

$0 - 1 = - 1$

Subtract $1$ from $0$ .

$- 1 = - 1$

Since $- 1 = - 1$ , the equation will always be true for any value of $x$ .

All real numbers

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$