Solve for x 0.4(x+2)-0.6(x+2)=-0.2x-0.4

$0.4 (x + 2) - 0.6 (x + 2) = - 0.2 x - 0.4$

Step 1

Simplify $0.4 (x + 2) - 0.6 (x + 2)$ .

Simplify each term.

Apply the distributive property.

$0.4 x + 0.4 \cdot 2 - 0.6 (x + 2) = - 0.2 x - 0.4$

Multiply $0.4$ by $2$ .

$0.4 x + 0.8 - 0.6 (x + 2) = - 0.2 x - 0.4$

Apply the distributive property.

$0.4 x + 0.8 - 0.6 x - 0.6 \cdot 2 = - 0.2 x - 0.4$

Multiply $- 0.6$ by $2$ .

$0.4 x + 0.8 - 0.6 x - 1.2 = - 0.2 x - 0.4$

Simplify by adding terms.

Subtract $0.6 x$ from $0.4 x$ .

$- 0.2 x + 0.8 - 1.2 = - 0.2 x - 0.4$

Subtract $1.2$ from $0.8$ .

$- 0.2 x - 0.4 = - 0.2 x - 0.4$

Step 2

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

Add $0.2 x$ to both sides of the equation.

$- 0.2 x - 0.4 + 0.2 x = - 0.4$

Add $- 0.2 x$ and $0.2 x$ .

$0 x - 0.4 = - 0.4$

Multiply $0$ by $x$ .

$0 - 0.4 = - 0.4$

Subtract $0.4$ from $0$ .

$- 0.4 = - 0.4$

Step 3

Since $- 0.4 = - 0.4$ , the equation will always be true for any value of $x$ .

All real numbers

Step 4

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$