Solve for x -(x-4)+5(2x+1)=4(2x-2)+14

$- (x - 4) + 5 (2 x + 1) = 4 (2 x - 2) + 14$

Step 1

Simplify $- (x - 4) + 5 (2 x + 1)$ .

Simplify each term.

Apply the distributive property.

$- x - - 4 + 5 (2 x + 1) = 4 (2 x - 2) + 14$

Multiply $- 1$ by $- 4$ .

$- x + 4 + 5 (2 x + 1) = 4 (2 x - 2) + 14$

Apply the distributive property.

$- x + 4 + 5 (2 x) + 5 \cdot 1 = 4 (2 x - 2) + 14$

Multiply $2$ by $5$ .

$- x + 4 + 10 x + 5 \cdot 1 = 4 (2 x - 2) + 14$

Multiply $5$ by $1$ .

$- x + 4 + 10 x + 5 = 4 (2 x - 2) + 14$

Simplify by adding terms.

Add $- x$ and $10 x$ .

$9 x + 4 + 5 = 4 (2 x - 2) + 14$

Add $4$ and $5$ .

$9 x + 9 = 4 (2 x - 2) + 14$

Step 2

Simplify $4 (2 x - 2) + 14$ .

Simplify each term.

Apply the distributive property.

$9 x + 9 = 4 (2 x) + 4 \cdot - 2 + 14$

Multiply $2$ by $4$ .

$9 x + 9 = 8 x + 4 \cdot - 2 + 14$

Multiply $4$ by $- 2$ .

$9 x + 9 = 8 x - 8 + 14$

Add $- 8$ and $14$ .

$9 x + 9 = 8 x + 6$

Step 3

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

Subtract $8 x$ from both sides of the equation.

$9 x + 9 - 8 x = 6$

Subtract $8 x$ from $9 x$ .

$x + 9 = 6$

Step 4

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

Subtract $9$ from both sides of the equation.

$x = 6 - 9$

Subtract $9$ from $6$ .

$x = - 3$