Solve for x 4.5(8-x)+36=102-2.5(3x+24)

$4.5 (8 - x) + 36 = 102 - 2.5 (3 x + 24)$

Simplify $4.5 (8 - x) + 36$ .

Simplify each term.

Apply the distributive property.

$4.5 \cdot 8 + 4.5 (- x) + 36 = 102 - 2.5 (3 x + 24)$

Multiply $4.5$ by $8$ .

$36 + 4.5 (- x) + 36 = 102 - 2.5 (3 x + 24)$

Multiply $- 1$ by $4.5$ .

$36 - 4.5 x + 36 = 102 - 2.5 (3 x + 24)$

Add $36$ and $36$ .

$- 4.5 x + 72 = 102 - 2.5 (3 x + 24)$

Simplify $102 - 2.5 (3 x + 24)$ .

Simplify each term.

Apply the distributive property.

$- 4.5 x + 72 = 102 - 2.5 (3 x) - 2.5 \cdot 24$

Multiply $3$ by $- 2.5$ .

$- 4.5 x + 72 = 102 - 7.5 x - 2.5 \cdot 24$

Multiply $- 2.5$ by $24$ .

$- 4.5 x + 72 = 102 - 7.5 x - 60$

Subtract $60$ from $102$ .

$- 4.5 x + 72 = - 7.5 x + 42$

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

Add $7.5 x$ to both sides of the equation.

$- 4.5 x + 72 + 7.5 x = 42$

Add $- 4.5 x$ and $7.5 x$ .

$3 x + 72 = 42$

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

Subtract $72$ from both sides of the equation.

$3 x = 42 - 72$

Subtract $72$ from $42$ .

$3 x = - 30$

Divide each term in $3 x = - 30$ by $3$ and simplify.

Divide each term in $3 x = - 30$ by $3$ .

$\frac{3 x}{3} = \frac{- 30}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{- 30}{3}$

Divide $x$ by $1$ .

$x = \frac{- 30}{3}$

Simplify the right side.

Divide $- 30$ by $3$ .

$x = - 10$