Solve the Inequality for d -9d-4(-3d-3)>=6d+6+6d

$- 9 d - 4 (- 3 d - 3) \geq 6 d + 6 + 6 d$

Simplify $- 9 d - 4 (- 3 d - 3)$ .

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Simplify each term.

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Apply the distributive property.

$- 9 d - 4 (- 3 d) - 4 \cdot - 3 \geq 6 d + 6 + 6 d$

Multiply $- 3$ by $- 4$ .

$- 9 d + 12 d - 4 \cdot - 3 \geq 6 d + 6 + 6 d$

Multiply $- 4$ by $- 3$ .

$- 9 d + 12 d + 12 \geq 6 d + 6 + 6 d$

Add $- 9 d$ and $12 d$ .

$3 d + 12 \geq 6 d + 6 + 6 d$

Add $6 d$ and $6 d$ .

$3 d + 12 \geq 12 d + 6$

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

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Subtract $12 d$ from both sides of the inequality.

$3 d + 12 - 12 d \geq 6$

Subtract $12 d$ from $3 d$ .

$- 9 d + 12 \geq 6$

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

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Subtract $12$ from both sides of the inequality.

$- 9 d \geq 6 - 12$

Subtract $12$ from $6$ .

$- 9 d \geq - 6$

Divide each term in $- 9 d \geq - 6$ by $- 9$ and simplify.

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Divide each term in $- 9 d \geq - 6$ by $- 9$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 9 d}{- 9} \leq \frac{- 6}{- 9}$

Simplify the left side.

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Cancel the common factor of $- 9$ .

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Cancel the common factor.

$\frac{- 9 d}{- 9} \leq \frac{- 6}{- 9}$

Divide $d$ by $1$ .

$d \leq \frac{- 6}{- 9}$

Simplify the right side.

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Cancel the common factor of $- 6$ and $- 9$ .

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Factor $- 3$ out of $- 6$ .

$d \leq \frac{- 3 (2)}{- 9}$

Cancel the common factors.

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Factor $- 3$ out of $- 9$ .

$d \leq \frac{- 3 \cdot 2}{- 3 \cdot 3}$

Cancel the common factor.

$d \leq \frac{- 3 \cdot 2}{- 3 \cdot 3}$

Rewrite the expression.

$d \leq \frac{2}{3}$

The result can be shown in multiple forms.

Inequality Form:

$d \leq \frac{2}{3}$

Interval Notation:

$(- \infty, \frac{2}{3}]$