Solve for x 2(x-3)+5=3(x-1)

$2 (x - 3) + 5 = 3 (x - 1)$

Step 1

Simplify $2 (x - 3) + 5$ .

Simplify each term.

Apply the distributive property.

$2 x + 2 \cdot - 3 + 5 = 3 (x - 1)$

Multiply $2$ by $- 3$ .

$2 x - 6 + 5 = 3 (x - 1)$

Add $- 6$ and $5$ .

$2 x - 1 = 3 (x - 1)$

Step 2

Simplify $3 (x - 1)$ .

Apply the distributive property.

$2 x - 1 = 3 x + 3 \cdot - 1$

Multiply $3$ by $- 1$ .

$2 x - 1 = 3 x - 3$

Step 3

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

Subtract $3 x$ from both sides of the equation.

$2 x - 1 - 3 x = - 3$

Subtract $3 x$ from $2 x$ .

$- x - 1 = - 3$

Step 4

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

Add $1$ to both sides of the equation.

$- x = - 3 + 1$

Add $- 3$ and $1$ .

$- x = - 2$

Step 5

Divide each term in $- x = - 2$ by $- 1$ and simplify.

Divide each term in $- x = - 2$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 2}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 2}{- 1}$

Divide $x$ by $1$ .

$x = \frac{- 2}{- 1}$

Simplify the right side.

Divide $- 2$ by $- 1$ .

$x = 2$