Solve for x 1.5(x+4)-3=4.5(x-2)

$1.5 (x + 4) - 3 = 4.5 (x - 2)$

Step 1

Simplify $1.5 (x + 4) - 3$ .

Simplify each term.

Apply the distributive property.

$1.5 x + 1.5 \cdot 4 - 3 = 4.5 (x - 2)$

Multiply $1.5$ by $4$ .

$1.5 x + 6 - 3 = 4.5 (x - 2)$

Subtract $3$ from $6$ .

$1.5 x + 3 = 4.5 (x - 2)$

Step 2

Simplify $4.5 (x - 2)$ .

Apply the distributive property.

$1.5 x + 3 = 4.5 x + 4.5 \cdot - 2$

Multiply $4.5$ by $- 2$ .

$1.5 x + 3 = 4.5 x - 9$

Step 3

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

Subtract $4.5 x$ from both sides of the equation.

$1.5 x + 3 - 4.5 x = - 9$

Subtract $4.5 x$ from $1.5 x$ .

$- 3 x + 3 = - 9$

Step 4

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

Subtract $3$ from both sides of the equation.

$- 3 x = - 9 - 3$

Subtract $3$ from $- 9$ .

$- 3 x = - 12$

Step 5

Divide each term in $- 3 x = - 12$ by $- 3$ and simplify.

Divide each term in $- 3 x = - 12$ by $- 3$ .

$\frac{- 3 x}{- 3} = \frac{- 12}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 x}{- 3} = \frac{- 12}{- 3}$

Divide $x$ by $1$ .

$x = \frac{- 12}{- 3}$

Simplify the right side.

Divide $- 12$ by $- 3$ .

$x = 4$