Solve for x 12+7x-9=3x+5-4(2-x)

$12 + 7 x - 9 = 3 x + 5 - 4 (2 - x)$

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.

$3 x + 5 - 4 (2 - x) = 12 + 7 x - 9$

Step 2

Simplify $3 x + 5 - 4 (2 - x)$ .

Simplify each term.

Apply the distributive property.

$3 x + 5 - 4 \cdot 2 - 4 (- x) = 12 + 7 x - 9$

Multiply $- 4$ by $2$ .

$3 x + 5 - 8 - 4 (- x) = 12 + 7 x - 9$

Multiply $- 1$ by $- 4$ .

$3 x + 5 - 8 + 4 x = 12 + 7 x - 9$

Simplify by adding terms.

Add $3 x$ and $4 x$ .

$7 x + 5 - 8 = 12 + 7 x - 9$

Subtract $8$ from $5$ .

$7 x - 3 = 12 + 7 x - 9$

Step 3

Subtract $9$ from $12$ .

$7 x - 3 = 7 x + 3$

Step 4

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

Subtract $7 x$ from both sides of the equation.

$7 x - 3 - 7 x = 3$

Combine the opposite terms in $7 x - 3 - 7 x$ .

Subtract $7 x$ from $7 x$ .

$0 - 3 = 3$

Subtract $3$ from $0$ .

$- 3 = 3$

Step 5

Since $- 3 \neq 3$ , there are no solutions.

No solution