Solve the Inequality for d -4-4(-2d-4)<=d+4-9

$- 4 - 4 (- 2 d - 4) \leq d + 4 - 9$

Simplify $- 4 - 4 (- 2 d - 4)$ .

Simplify each term.

Apply the distributive property.

$- 4 - 4 (- 2 d) - 4 \cdot - 4 \leq d + 4 - 9$

Multiply $- 2$ by $- 4$ .

$- 4 + 8 d - 4 \cdot - 4 \leq d + 4 - 9$

Multiply $- 4$ by $- 4$ .

$- 4 + 8 d + 16 \leq d + 4 - 9$

Add $- 4$ and $16$ .

$8 d + 12 \leq d + 4 - 9$

Subtract $9$ from $4$ .

$8 d + 12 \leq d - 5$

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

Subtract $d$ from both sides of the inequality.

$8 d + 12 - d \leq - 5$

Subtract $d$ from $8 d$ .

$7 d + 12 \leq - 5$

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

Subtract $12$ from both sides of the inequality.

$7 d \leq - 5 - 12$

Subtract $12$ from $- 5$ .

$7 d \leq - 17$

Divide each term in $7 d \leq - 17$ by $7$ and simplify.

Divide each term in $7 d \leq - 17$ by $7$ .

$\frac{7 d}{7} \leq \frac{- 17}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 d}{7} \leq \frac{- 17}{7}$

Divide $d$ by $1$ .

$d \leq \frac{- 17}{7}$

Simplify the right side.

Move the negative in front of the fraction.

$d \leq - \frac{17}{7}$

The result can be shown in multiple forms.

Inequality Form:

$d \leq - \frac{17}{7}$

Interval Notation:

$(- \infty, - \frac{17}{7}]$