Solve for x 9(x-2)=5(2+x)

$9 (x - 2) = 5 (2 + x)$

Step 1

Simplify $9 (x - 2)$ .

Rewrite.

$0 + 0 + 9 (x - 2) = 5 (2 + x)$

Simplify by adding zeros.

$9 (x - 2) = 5 (2 + x)$

Apply the distributive property.

$9 x + 9 \cdot - 2 = 5 (2 + x)$

Multiply $9$ by $- 2$ .

$9 x - 18 = 5 (2 + x)$

Step 2

Simplify $5 (2 + x)$ .

Apply the distributive property.

$9 x - 18 = 5 \cdot 2 + 5 x$

Multiply $5$ by $2$ .

$9 x - 18 = 10 + 5 x$

Step 3

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

Subtract $5 x$ from both sides of the equation.

$9 x - 18 - 5 x = 10$

Subtract $5 x$ from $9 x$ .

$4 x - 18 = 10$

Step 4

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

Add $18$ to both sides of the equation.

$4 x = 10 + 18$

Add $10$ and $18$ .

$4 x = 28$

Step 5

Divide each term in $4 x = 28$ by $4$ and simplify.

Divide each term in $4 x = 28$ by $4$ .

$\frac{4 x}{4} = \frac{28}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{28}{4}$

Divide $x$ by $1$ .

$x = \frac{28}{4}$

Simplify the right side.

Divide $28$ by $4$ .

$x = 7$