Solve for x 2(x-3)-17=13-3(x+2)

$2 (x - 3) - 17 = 13 - 3 (x + 2)$

Step 1

Simplify $2 (x - 3) - 17$ .

Simplify each term.

Apply the distributive property.

$2 x + 2 \cdot - 3 - 17 = 13 - 3 (x + 2)$

Multiply $2$ by $- 3$ .

$2 x - 6 - 17 = 13 - 3 (x + 2)$

Subtract $17$ from $- 6$ .

$2 x - 23 = 13 - 3 (x + 2)$

Step 2

Simplify $13 - 3 (x + 2)$ .

Simplify each term.

Apply the distributive property.

$2 x - 23 = 13 - 3 x - 3 \cdot 2$

Multiply $- 3$ by $2$ .

$2 x - 23 = 13 - 3 x - 6$

Subtract $6$ from $13$ .

$2 x - 23 = - 3 x + 7$

Step 3

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

Add $3 x$ to both sides of the equation.

$2 x - 23 + 3 x = 7$

Add $2 x$ and $3 x$ .

$5 x - 23 = 7$

Step 4

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

Add $23$ to both sides of the equation.

$5 x = 7 + 23$

Add $7$ and $23$ .

$5 x = 30$

Step 5

Divide each term in $5 x = 30$ by $5$ and simplify.

Divide each term in $5 x = 30$ by $5$ .

$\frac{5 x}{5} = \frac{30}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{30}{5}$

Divide $x$ by $1$ .

$x = \frac{30}{5}$

Simplify the right side.

Divide $30$ by $5$ .

$x = 6$