Solve the Inequality for q -9q-(-3q+3)>=6q-7-7

$- 9 q - (- 3 q + 3) \geq 6 q - 7 - 7$

Simplify $- 9 q - (- 3 q + 3)$ .

Simplify each term.

Apply the distributive property.

$- 9 q - (- 3 q) - 1 \cdot 3 \geq 6 q - 7 - 7$

Multiply $- 3$ by $- 1$ .

$- 9 q + 3 q - 1 \cdot 3 \geq 6 q - 7 - 7$

Multiply $- 1$ by $3$ .

$- 9 q + 3 q - 3 \geq 6 q - 7 - 7$

Add $- 9 q$ and $3 q$ .

$- 6 q - 3 \geq 6 q - 7 - 7$

Subtract $7$ from $- 7$ .

$- 6 q - 3 \geq 6 q - 14$

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

Subtract $6 q$ from both sides of the inequality.

$- 6 q - 3 - 6 q \geq - 14$

Subtract $6 q$ from $- 6 q$ .

$- 12 q - 3 \geq - 14$

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

Add $3$ to both sides of the inequality.

$- 12 q \geq - 14 + 3$

Add $- 14$ and $3$ .

$- 12 q \geq - 11$

Divide each term in $- 12 q \geq - 11$ by $- 12$ and simplify.

Divide each term in $- 12 q \geq - 11$ by $- 12$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 12 q}{- 12} \leq \frac{- 11}{- 12}$

Simplify the left side.

Cancel the common factor of $- 12$ .

Cancel the common factor.

$\frac{- 12 q}{- 12} \leq \frac{- 11}{- 12}$

Divide $q$ by $1$ .

$q \leq \frac{- 11}{- 12}$

Simplify the right side.

Dividing two negative values results in a positive value.

$q \leq \frac{11}{12}$

The result can be shown in multiple forms.

Inequality Form:

$q \leq \frac{11}{12}$

Interval Notation:

$(- \infty, \frac{11}{12}]$

Solve the Inequality for q -9q-(-3q+3)>=6q-7-7

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