Solve for x 5(x+1)-3x=5-2(5-x)

$5 (x + 1) - 3 x = 5 - 2 (5 - x)$

Step 1

Simplify $5 (x + 1) - 3 x$ .

Simplify each term.

Apply the distributive property.

$5 x + 5 \cdot 1 - 3 x = 5 - 2 (5 - x)$

Multiply $5$ by $1$ .

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

Subtract $3 x$ from $5 x$ .

$2 x + 5 = 5 - 2 (5 - x)$

Step 2

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

Simplify each term.

Apply the distributive property.

$2 x + 5 = 5 - 2 \cdot 5 - 2 (- x)$

Multiply $- 2$ by $5$ .

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

Multiply $- 1$ by $- 2$ .

$2 x + 5 = 5 - 10 + 2 x$

Subtract $10$ from $5$ .

$2 x + 5 = - 5 + 2 x$

Step 3

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

Subtract $2 x$ from both sides of the equation.

$2 x + 5 - 2 x = - 5$

Combine the opposite terms in $2 x + 5 - 2 x$ .

Subtract $2 x$ from $2 x$ .

$0 + 5 = - 5$

Add $0$ and $5$ .

$5 = - 5$

Step 4

Since $5 \neq - 5$ , there are no solutions.

No solution