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

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

Simplify $3 (6 + x)$ .

Rewrite.

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

Simplify by adding zeros.

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

Apply the distributive property.

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

Multiply $3$ by $6$ .

$- x + 6 > 18 + 3 x$

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

Subtract $3 x$ from both sides of the inequality.

$- x + 6 - 3 x > 18$

Subtract $3 x$ from $- x$ .

$- 4 x + 6 > 18$

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

Subtract $6$ from both sides of the inequality.

$- 4 x > 18 - 6$

Subtract $6$ from $18$ .

$- 4 x > 12$

Divide each term in $- 4 x > 12$ by $- 4$ and simplify.

Divide each term in $- 4 x > 12$ by $- 4$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 4 x}{- 4} < \frac{12}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 x}{- 4} < \frac{12}{- 4}$

Divide $x$ by $1$ .

$x < \frac{12}{- 4}$

Simplify the right side.

Divide $12$ by $- 4$ .

$x < - 3$

The result can be shown in multiple forms.

Inequality Form:

$x < - 3$

Interval Notation:

$(- \infty, - 3)$

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

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