Solve for x 2(2+x)-(6-7x)=13x-(1+4x)

$2 (2 + x) - (6 - 7 x) = 13 x - (1 + 4 x)$

Step 1

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

Simplify each term.

Apply the distributive property.

$2 \cdot 2 + 2 x - (6 - 7 x) = 13 x - (1 + 4 x)$

Multiply $2$ by $2$ .

$4 + 2 x - (6 - 7 x) = 13 x - (1 + 4 x)$

Apply the distributive property.

$4 + 2 x - 1 \cdot 6 - (- 7 x) = 13 x - (1 + 4 x)$

Multiply $- 1$ by $6$ .

$4 + 2 x - 6 - (- 7 x) = 13 x - (1 + 4 x)$

Multiply $- 7$ by $- 1$ .

$4 + 2 x - 6 + 7 x = 13 x - (1 + 4 x)$

Simplify by adding terms.

Subtract $6$ from $4$ .

$2 x - 2 + 7 x = 13 x - (1 + 4 x)$

Add $2 x$ and $7 x$ .

$9 x - 2 = 13 x - (1 + 4 x)$

Step 2

Simplify $13 x - (1 + 4 x)$ .

Simplify each term.

Apply the distributive property.

$9 x - 2 = 13 x - 1 \cdot 1 - (4 x)$

Multiply $- 1$ by $1$ .

$9 x - 2 = 13 x - 1 - (4 x)$

Multiply $4$ by $- 1$ .

$9 x - 2 = 13 x - 1 - 4 x$

Subtract $4 x$ from $13 x$ .

$9 x - 2 = 9 x - 1$

Step 3

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

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

$9 x - 2 - 9 x = - 1$

Combine the opposite terms in $9 x - 2 - 9 x$ .

Subtract $9 x$ from $9 x$ .

$0 - 2 = - 1$

Subtract $2$ from $0$ .

$- 2 = - 1$

Step 4

Since $- 2 \neq - 1$ , there are no solutions.

No solution