Solve for x 2/3(6x+6)=4x+4

$\frac{2}{3} (6 x + 6) = 4 x + 4$

Simplify $\frac{2}{3} \cdot (6 x + 6)$ .

Rewrite.

$0 + 0 + \frac{2}{3} \cdot (6 x + 6) = 4 x + 4$

Simplify by adding zeros.

$\frac{2}{3} \cdot (6 x + 6) = 4 x + 4$

Apply the distributive property.

$\frac{2}{3} (6 x) + \frac{2}{3} \cdot 6 = 4 x + 4$

Cancel the common factor of $3$ .

Factor $3$ out of $6 x$ .

$\frac{2}{3} (3 (2 x)) + \frac{2}{3} \cdot 6 = 4 x + 4$

Cancel the common factor.

$\frac{2}{3} (3 (2 x)) + \frac{2}{3} \cdot 6 = 4 x + 4$

Rewrite the expression.

$2 (2 x) + \frac{2}{3} \cdot 6 = 4 x + 4$

Multiply $2$ by $2$ .

$4 x + \frac{2}{3} \cdot 6 = 4 x + 4$

Cancel the common factor of $3$ .

Factor $3$ out of $6$ .

$4 x + \frac{2}{3} \cdot (3 (2)) = 4 x + 4$

Cancel the common factor.

$4 x + \frac{2}{3} \cdot (3 \cdot 2) = 4 x + 4$

Rewrite the expression.

$4 x + 2 \cdot 2 = 4 x + 4$

Multiply $2$ by $2$ .

$4 x + 4 = 4 x + 4$

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

Subtract $4 x$ from both sides of the equation.

$4 x + 4 - 4 x = 4$

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

Subtract $4 x$ from $4 x$ .

$0 + 4 = 4$

Add $0$ and $4$ .

$4 = 4$

Since $4 = 4$ , the equation will always be true for any value of $x$ .

All real numbers

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$