Solve for x 3x-2(6-x)=7x+2(5+x)-6

$3 x - 2 (6 - x) = 7 x + 2 (5 + x) - 6$

Step 1

Simplify $3 x - 2 (6 - x)$ .

Simplify each term.

Apply the distributive property.

$3 x - 2 \cdot 6 - 2 (- x) = 7 x + 2 (5 + x) - 6$

Multiply $- 2$ by $6$ .

$3 x - 12 - 2 (- x) = 7 x + 2 (5 + x) - 6$

Multiply $- 1$ by $- 2$ .

$3 x - 12 + 2 x = 7 x + 2 (5 + x) - 6$

Add $3 x$ and $2 x$ .

$5 x - 12 = 7 x + 2 (5 + x) - 6$

Step 2

Simplify $7 x + 2 (5 + x) - 6$ .

Simplify each term.

Apply the distributive property.

$5 x - 12 = 7 x + 2 \cdot 5 + 2 x - 6$

Multiply $2$ by $5$ .

$5 x - 12 = 7 x + 10 + 2 x - 6$

Simplify by adding terms.

Add $7 x$ and $2 x$ .

$5 x - 12 = 9 x + 10 - 6$

Subtract $6$ from $10$ .

$5 x - 12 = 9 x + 4$

Step 3

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

Subtract $9 x$ from both sides of the equation.

$5 x - 12 - 9 x = 4$

Subtract $9 x$ from $5 x$ .

$- 4 x - 12 = 4$

Step 4

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

Add $12$ to both sides of the equation.

$- 4 x = 4 + 12$

Add $4$ and $12$ .

$- 4 x = 16$

Step 5

Divide each term in $- 4 x = 16$ by $- 4$ and simplify.

Divide each term in $- 4 x = 16$ by $- 4$ .

$\frac{- 4 x}{- 4} = \frac{16}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 x}{- 4} = \frac{16}{- 4}$

Divide $x$ by $1$ .

$x = \frac{16}{- 4}$

Simplify the right side.

Divide $16$ by $- 4$ .

$x = - 4$

Solve for x 3x-2(6-x)=7x+2(5+x)-6

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