Solve for x 3x+2>(3x-6)/3

$3 x + 2 > \frac{3 x - 6}{3}$

Cancel the common factor of $3 x - 6$ and $3$ .

Factor $3$ out of $3 x$ .

$3 x + 2 > \frac{3 (x) - 6}{3}$

Factor $3$ out of $- 6$ .

$3 x + 2 > \frac{3 (x) + 3 \cdot - 2}{3}$

Factor $3$ out of $3 (x) + 3 (- 2)$ .

$3 x + 2 > \frac{3 (x - 2)}{3}$

Cancel the common factors.

Factor $3$ out of $3$ .

$3 x + 2 > \frac{3 (x - 2)}{3 (1)}$

Cancel the common factor.

$3 x + 2 > \frac{3 (x - 2)}{3 \cdot 1}$

Rewrite the expression.

$3 x + 2 > \frac{x - 2}{1}$

Divide $x - 2$ by $1$ .

$3 x + 2 > x - 2$

Solve for $x$ .

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

Subtract $x$ from both sides of the inequality.

$3 x + 2 - x > - 2$

Subtract $x$ from $3 x$ .

$2 x + 2 > - 2$

Move all terms not containing $x$ to the right side of the inequality.

Subtract $2$ from both sides of the inequality.

$2 x > - 2 - 2$

Subtract $2$ from $- 2$ .

$2 x > - 4$

Divide each term in $2 x > - 4$ by $2$ and simplify.

Divide each term in $2 x > - 4$ by $2$ .

$\frac{2 x}{2} > \frac{- 4}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} > \frac{- 4}{2}$

Divide $x$ by $1$ .

$x > \frac{- 4}{2}$

Simplify the right side.

Divide $- 4$ by $2$ .

$x > - 2$

The result can be shown in multiple forms.

Inequality Form:

$x > - 2$

Interval Notation:

$(- 2, \infty)$