Solve by Factoring 5(2+x)-x=10+4(x+1)

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

Step 1

Move all the expressions to the left side of the equation.

Subtract $10$ from both sides of the equation.

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

Subtract $4 (x + 1)$ from both sides of the equation.

$5 (2 + x) - x - 10 - 4 (x + 1) = 0$

Step 2

Simplify $5 (2 + x) - x - 10 - 4 (x + 1)$ .

Simplify each term.

Apply the distributive property.

$5 \cdot 2 + 5 x - x - 10 - 4 (x + 1) = 0$

Multiply $5$ by $2$ .

$10 + 5 x - x - 10 - 4 (x + 1) = 0$

Apply the distributive property.

$10 + 5 x - x - 10 - 4 x - 4 \cdot 1 = 0$

Multiply $- 4$ by $1$ .

$10 + 5 x - x - 10 - 4 x - 4 = 0$

Combine the opposite terms in $10 + 5 x - x - 10 - 4 x - 4$ .

Subtract $10$ from $10$ .

$5 x - x + 0 - 4 x - 4 = 0$

Add $5 x - x$ and $0$ .

$5 x - x - 4 x - 4 = 0$

Subtract $x$ from $5 x$ .

$4 x - 4 x - 4 = 0$

Subtract $4 x$ from $4 x$ .

$0 - 4 = 0$

Subtract $4$ from $0$ .

$- 4 = 0$

Step 3

Since $- 4 \neq 0$ , there are no solutions.

No solution