Solve for x 0.5(x+3)-0.8(x+3)=-0.3x-0.9

$0.5 (x + 3) - 0.8 (x + 3) = - 0.3 x - 0.9$

Step 1

Simplify $0.5 (x + 3) - 0.8 (x + 3)$ .

Simplify each term.

Apply the distributive property.

$0.5 x + 0.5 \cdot 3 - 0.8 (x + 3) = - 0.3 x - 0.9$

Multiply $0.5$ by $3$ .

$0.5 x + 1.5 - 0.8 (x + 3) = - 0.3 x - 0.9$

Apply the distributive property.

$0.5 x + 1.5 - 0.8 x - 0.8 \cdot 3 = - 0.3 x - 0.9$

Multiply $- 0.8$ by $3$ .

$0.5 x + 1.5 - 0.8 x - 2.4 = - 0.3 x - 0.9$

Simplify by adding terms.

Subtract $0.8 x$ from $0.5 x$ .

$- 0.3 x + 1.5 - 2.4 = - 0.3 x - 0.9$

Subtract $2.4$ from $1.5$ .

$- 0.3 x - 0.9 = - 0.3 x - 0.9$

Step 2

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

Add $0.3 x$ to both sides of the equation.

$- 0.3 x - 0.9 + 0.3 x = - 0.9$

Add $- 0.3 x$ and $0.3 x$ .

$0 x - 0.9 = - 0.9$

Multiply $0$ by $x$ .

$0 - 0.9 = - 0.9$

Subtract $0.9$ from $0$ .

$- 0.9 = - 0.9$

Step 3

Since $- 0.9 = - 0.9$ , 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:

$(- \infty, \infty)$