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

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

Step 1

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

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

Step 2

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

Simplify each term.

Apply the distributive property.

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

Multiply $3$ by $2$ .

$3 x + 6 - x = 3 x - 1$

Subtract $x$ from $3 x$ .

$2 x + 6 = 3 x - 1$

Step 3

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

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

$2 x + 6 - 3 x = - 1$

Subtract $3 x$ from $2 x$ .

$- x + 6 = - 1$

Step 4

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

Subtract $6$ from both sides of the equation.

$- x = - 1 - 6$

Subtract $6$ from $- 1$ .

$- x = - 7$

Step 5

Divide each term in $- x = - 7$ by $- 1$ and simplify.

Divide each term in $- x = - 7$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 7}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 7}{- 1}$

Divide $x$ by $1$ .

$x = \frac{- 7}{- 1}$

Simplify the right side.

Divide $- 7$ by $- 1$ .

$x = 7$