Solve the Inequality for d -5d-(-9d+7)>=-d+10+9d

$- 5 d - (- 9 d + 7) \geq - d + 10 + 9 d$

Simplify $- 5 d - (- 9 d + 7)$ .

Simplify each term.

Apply the distributive property.

$- 5 d - (- 9 d) - 1 \cdot 7 \geq - d + 10 + 9 d$

Multiply $- 9$ by $- 1$ .

$- 5 d + 9 d - 1 \cdot 7 \geq - d + 10 + 9 d$

Multiply $- 1$ by $7$ .

$- 5 d + 9 d - 7 \geq - d + 10 + 9 d$

Add $- 5 d$ and $9 d$ .

$4 d - 7 \geq - d + 10 + 9 d$

Add $- d$ and $9 d$ .

$4 d - 7 \geq 8 d + 10$

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

Subtract $8 d$ from both sides of the inequality.

$4 d - 7 - 8 d \geq 10$

Subtract $8 d$ from $4 d$ .

$- 4 d - 7 \geq 10$

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

Add $7$ to both sides of the inequality.

$- 4 d \geq 10 + 7$

Add $10$ and $7$ .

$- 4 d \geq 17$

Divide each term in $- 4 d \geq 17$ by $- 4$ and simplify.

Divide each term in $- 4 d \geq 17$ by $- 4$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 4 d}{- 4} \leq \frac{17}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 d}{- 4} \leq \frac{17}{- 4}$

Divide $d$ by $1$ .

$d \leq \frac{17}{- 4}$

Simplify the right side.

Move the negative in front of the fraction.

$d \leq - \frac{17}{4}$

The result can be shown in multiple forms.

Inequality Form:

$d \leq - \frac{17}{4}$

Interval Notation:

$(- \infty, - \frac{17}{4}]$

Solve the Inequality for d -5d-(-9d+7)>=-d+10+9d

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