Solve for x 1.2(x+5)=1.6(2x+5)

$1.2 (x + 5) = 1.6 (2 x + 5)$

Step 1

Simplify $1.2 (x + 5)$ .

Rewrite.

$0 + 0 + 1.2 (x + 5) = 1.6 (2 x + 5)$

Simplify by adding zeros.

$1.2 (x + 5) = 1.6 (2 x + 5)$

Apply the distributive property.

$1.2 x + 1.2 \cdot 5 = 1.6 (2 x + 5)$

Multiply $1.2$ by $5$ .

$1.2 x + 6 = 1.6 (2 x + 5)$

Step 2

Simplify $1.6 (2 x + 5)$ .

Apply the distributive property.

$1.2 x + 6 = 1.6 (2 x) + 1.6 \cdot 5$

Multiply.

Multiply $2$ by $1.6$ .

$1.2 x + 6 = 3.2 x + 1.6 \cdot 5$

Multiply $1.6$ by $5$ .

$1.2 x + 6 = 3.2 x + 8$

Step 3

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

Subtract $3.2 x$ from both sides of the equation.

$1.2 x + 6 - 3.2 x = 8$

Subtract $3.2 x$ from $1.2 x$ .

$- 2 x + 6 = 8$

Step 4

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

Subtract $6$ from both sides of the equation.

$- 2 x = 8 - 6$

Subtract $6$ from $8$ .

$- 2 x = 2$

Step 5

Divide each term in $- 2 x = 2$ by $- 2$ and simplify.

Divide each term in $- 2 x = 2$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{2}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{2}{- 2}$

Divide $x$ by $1$ .

$x = \frac{2}{- 2}$

Simplify the right side.

Divide $2$ by $- 2$ .

$x = - 1$