Solve the Inequality for x -2<=(6+x)/3

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

Multiply both sides by $3$ .

$- 2 \cdot 3 \leq \frac{6 + x}{3} \cdot 3$

Simplify.

Simplify the left side.

Multiply $- 2$ by $3$ .

$- 6 \leq \frac{6 + x}{3} \cdot 3$

Simplify the right side.

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

Cancel the common factor of $3$ .

Cancel the common factor.

$- 6 \leq \frac{6 + x}{3} \cdot 3$

Rewrite the expression.

$- 6 \leq 6 + x$

Reorder $6$ and $x$ .

$- 6 \leq x + 6$

Solve for $x$ .

Rewrite so $x$ is on the left side of the inequality.

$x + 6 \geq - 6$

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

Subtract $6$ from both sides of the inequality.

$x \geq - 6 - 6$

Subtract $6$ from $- 6$ .

$x \geq - 12$

The result can be shown in multiple forms.

Inequality Form:

$x \geq - 12$

Interval Notation:

$[- 12, \infty)$