Solve for x 10(x+1)=5(2x+2)

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

Step 1

Simplify $10 (x + 1)$ .

Rewrite.

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

Simplify by adding zeros.

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

Apply the distributive property.

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

Multiply $10$ by $1$ .

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

Step 2

Simplify $5 (2 x + 2)$ .

Apply the distributive property.

$10 x + 10 = 5 (2 x) + 5 \cdot 2$

Multiply.

Multiply $2$ by $5$ .

$10 x + 10 = 10 x + 5 \cdot 2$

Multiply $5$ by $2$ .

$10 x + 10 = 10 x + 10$

Step 3

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

Subtract $10 x$ from both sides of the equation.

$10 x + 10 - 10 x = 10$

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

Subtract $10 x$ from $10 x$ .

$0 + 10 = 10$

Add $0$ and $10$ .

$10 = 10$

Step 4

Since $10 = 10$ , the equation will always be true for any value of $x$ .

All real numbers

Step 5

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$