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

$- 2 (x + 3) > x + 6$

Simplify $- 2 (x + 3)$ .

Rewrite.

$0 + 0 - 2 (x + 3) > x + 6$

Simplify by adding zeros.

$- 2 (x + 3) > x + 6$

Apply the distributive property.

$- 2 x - 2 \cdot 3 > x + 6$

Multiply $- 2$ by $3$ .

$- 2 x - 6 > x + 6$

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

Subtract $x$ from both sides of the inequality.

$- 2 x - 6 - x > 6$

Subtract $x$ from $- 2 x$ .

$- 3 x - 6 > 6$

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

Add $6$ to both sides of the inequality.

$- 3 x > 6 + 6$

Add $6$ and $6$ .

$- 3 x > 12$

Divide each term in $- 3 x > 12$ by $- 3$ and simplify.

Divide each term in $- 3 x > 12$ by $- 3$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 3 x}{- 3} < \frac{12}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 x}{- 3} < \frac{12}{- 3}$

Divide $x$ by $1$ .

$x < \frac{12}{- 3}$

Simplify the right side.

Divide $12$ by $- 3$ .

$x < - 4$

The result can be shown in multiple forms.

Inequality Form:

$x < - 4$

Interval Notation:

$(- \infty, - 4)$

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

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