Solve for x 2(x-3)-7(5-x)=9x-45

$2 (x - 3) - 7 (5 - x) = 9 x - 45$

Simplify $2 (x - 3) - 7 (5 - x)$ .

Simplify each term.

Apply the distributive property.

$2 x + 2 \cdot - 3 - 7 (5 - x) = 9 x - 45$

Multiply $2$ by $- 3$ .

$2 x - 6 - 7 (5 - x) = 9 x - 45$

Apply the distributive property.

$2 x - 6 - 7 \cdot 5 - 7 (- x) = 9 x - 45$

Multiply $- 7$ by $5$ .

$2 x - 6 - 35 - 7 (- x) = 9 x - 45$

Multiply $- 1$ by $- 7$ .

$2 x - 6 - 35 + 7 x = 9 x - 45$

Simplify by adding terms.

Add $2 x$ and $7 x$ .

$9 x - 6 - 35 = 9 x - 45$

Subtract $35$ from $- 6$ .

$9 x - 41 = 9 x - 45$

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

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

$9 x - 41 - 9 x = - 45$

Combine the opposite terms in $9 x - 41 - 9 x$ .

Subtract $9 x$ from $9 x$ .

$0 - 41 = - 45$

Subtract $41$ from $0$ .

$- 41 = - 45$

Since $- 41 \neq - 45$ , there are no solutions.

No solution