Solve the Inequality for q -9-5(8q-9)<=-2q-9-2

$- 9 - 5 (8 q - 9) \leq - 2 q - 9 - 2$

Simplify $- 9 - 5 (8 q - 9)$ .

Simplify each term.

Apply the distributive property.

$- 9 - 5 (8 q) - 5 \cdot - 9 \leq - 2 q - 9 - 2$

Multiply $8$ by $- 5$ .

$- 9 - 40 q - 5 \cdot - 9 \leq - 2 q - 9 - 2$

Multiply $- 5$ by $- 9$ .

$- 9 - 40 q + 45 \leq - 2 q - 9 - 2$

Add $- 9$ and $45$ .

$- 40 q + 36 \leq - 2 q - 9 - 2$

Subtract $2$ from $- 9$ .

$- 40 q + 36 \leq - 2 q - 11$

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

Add $2 q$ to both sides of the inequality.

$- 40 q + 36 + 2 q \leq - 11$

Add $- 40 q$ and $2 q$ .

$- 38 q + 36 \leq - 11$

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

Subtract $36$ from both sides of the inequality.

$- 38 q \leq - 11 - 36$

Subtract $36$ from $- 11$ .

$- 38 q \leq - 47$

Divide each term in $- 38 q \leq - 47$ by $- 38$ and simplify.

Divide each term in $- 38 q \leq - 47$ by $- 38$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 38 q}{- 38} \geq \frac{- 47}{- 38}$

Simplify the left side.

Cancel the common factor of $- 38$ .

Cancel the common factor.

$\frac{- 38 q}{- 38} \geq \frac{- 47}{- 38}$

Divide $q$ by $1$ .

$q \geq \frac{- 47}{- 38}$

Simplify the right side.

Dividing two negative values results in a positive value.

$q \geq \frac{47}{38}$

The result can be shown in multiple forms.

Inequality Form:

$q \geq \frac{47}{38}$

Interval Notation:

$[\frac{47}{38}, \infty)$

Solve the Inequality for q -9-5(8q-9)<=-2q-9-2

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