Solve for x 0.4x+3=0.2(3x+1)-x

$0.4 x + 3 = 0.2 (3 x + 1) - x$

Step 1

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$0.2 (3 x + 1) - x = 0.4 x + 3$

Step 2

Simplify $0.2 (3 x + 1) - x$ .

Simplify each term.

Apply the distributive property.

$0.2 (3 x) + 0.2 \cdot 1 - x = 0.4 x + 3$

Multiply $3$ by $0.2$ .

$0.6 x + 0.2 \cdot 1 - x = 0.4 x + 3$

Multiply $0.2$ by $1$ .

$0.6 x + 0.2 - x = 0.4 x + 3$

Subtract $x$ from $0.6 x$ .

$- 0.4 x + 0.2 = 0.4 x + 3$

Step 3

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

Subtract $0.4 x$ from both sides of the equation.

$- 0.4 x + 0.2 - 0.4 x = 3$

Subtract $0.4 x$ from $- 0.4 x$ .

$- 0.8 x + 0.2 = 3$

Step 4

Move all terms not containing $x$ to the right side of the equation.

Subtract $0.2$ from both sides of the equation.

$- 0.8 x = 3 - 0.2$

Subtract $0.2$ from $3$ .

$- 0.8 x = 2.8$

Step 5

Divide each term in $- 0.8 x = 2.8$ by $- 0.8$ and simplify.

Divide each term in $- 0.8 x = 2.8$ by $- 0.8$ .

$\frac{- 0.8 x}{- 0.8} = \frac{2.8}{- 0.8}$

Simplify the left side.

Cancel the common factor of $- 0.8$ .

Cancel the common factor.

$\frac{- 0.8 x}{- 0.8} = \frac{2.8}{- 0.8}$

Divide $x$ by $1$ .

$x = \frac{2.8}{- 0.8}$

Simplify the right side.

Divide $2.8$ by $- 0.8$ .

$x = - 3.5$