Solve for x 0.2(x+3)-4(2x-3)=0.9

$0.2 (x + 3) - 4 (2 x - 3) = 0.9$

Step 1

Simplify $0.2 (x + 3) - 4 (2 x - 3)$ .

Simplify each term.

Apply the distributive property.

$0.2 x + 0.2 \cdot 3 - 4 (2 x - 3) = 0.9$

Multiply $0.2$ by $3$ .

$0.2 x + 0.6 - 4 (2 x - 3) = 0.9$

Apply the distributive property.

$0.2 x + 0.6 - 4 (2 x) - 4 \cdot - 3 = 0.9$

Multiply $2$ by $- 4$ .

$0.2 x + 0.6 - 8 x - 4 \cdot - 3 = 0.9$

Multiply $- 4$ by $- 3$ .

$0.2 x + 0.6 - 8 x + 12 = 0.9$

Simplify by adding terms.

Subtract $8 x$ from $0.2 x$ .

$- 7.8 x + 0.6 + 12 = 0.9$

Add $0.6$ and $12$ .

$- 7.8 x + 12.6 = 0.9$

Step 2

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

Subtract $12.6$ from both sides of the equation.

$- 7.8 x = 0.9 - 12.6$

Subtract $12.6$ from $0.9$ .

$- 7.8 x = - 11.7$

Step 3

Divide each term in $- 7.8 x = - 11.7$ by $- 7.8$ and simplify.

Divide each term in $- 7.8 x = - 11.7$ by $- 7.8$ .

$\frac{- 7.8 x}{- 7.8} = \frac{- 11.7}{- 7.8}$

Simplify the left side.

Cancel the common factor of $- 7.8$ .

Cancel the common factor.

$\frac{- 7.8 x}{- 7.8} = \frac{- 11.7}{- 7.8}$

Divide $x$ by $1$ .

$x = \frac{- 11.7}{- 7.8}$

Simplify the right side.

Divide $- 11.7$ by $- 7.8$ .

$x = 1.5$