Solve for x 16=3(x-1)-(x-7)

$16 = 3 (x - 1) - (x - 7)$

Step 1

Rewrite the equation as $3 (x - 1) - (x - 7) = 16$ .

$3 (x - 1) - (x - 7) = 16$

Step 2

Simplify $3 (x - 1) - (x - 7)$ .

Simplify each term.

Apply the distributive property.

$3 x + 3 \cdot - 1 - (x - 7) = 16$

Multiply $3$ by $- 1$ .

$3 x - 3 - (x - 7) = 16$

Apply the distributive property.

$3 x - 3 - x - - 7 = 16$

Multiply $- 1$ by $- 7$ .

$3 x - 3 - x + 7 = 16$

Simplify by adding terms.

Subtract $x$ from $3 x$ .

$2 x - 3 + 7 = 16$

Add $- 3$ and $7$ .

$2 x + 4 = 16$

Step 3

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

Subtract $4$ from both sides of the equation.

$2 x = 16 - 4$

Subtract $4$ from $16$ .

$2 x = 12$

Step 4

Divide each term in $2 x = 12$ by $2$ and simplify.

Divide each term in $2 x = 12$ by $2$ .

$\frac{2 x}{2} = \frac{12}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{12}{2}$

Divide $x$ by $1$ .

$x = \frac{12}{2}$

Simplify the right side.

Divide $12$ by $2$ .

$x = 6$