Solve the Inequality for x (2(x-3))/6>-2

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

Step 1

Cancel the common factors.

Factor $2$ out of $6$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 2

Multiply both sides by $3$ .

$\frac{x - 3}{3} \cdot 3 > - 2 \cdot 3$

Step 3

Simplify.

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{x - 3}{3} \cdot 3 > - 2 \cdot 3$

Rewrite the expression.

$x - 3 > - 2 \cdot 3$

Simplify the right side.

Multiply $- 2$ by $3$ .

$x - 3 > - 6$

Step 4

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

Add $3$ to both sides of the inequality.

$x > - 6 + 3$

Add $- 6$ and $3$ .

$x > - 3$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x > - 3$

Interval Notation:

$(- 3, \infty)$