Solve the Inequality for q 2(q-3)+6<=-10

$2 (q - 3) + 6 \leq - 10$

Simplify $2 (q - 3) + 6$ .

Simplify each term.

Apply the distributive property.

$2 q + 2 \cdot - 3 + 6 \leq - 10$

Multiply $2$ by $- 3$ .

$2 q - 6 + 6 \leq - 10$

Combine the opposite terms in $2 q - 6 + 6$ .

Add $- 6$ and $6$ .

$2 q + 0 \leq - 10$

Add $2 q$ and $0$ .

$2 q \leq - 10$

Divide each term in $2 q \leq - 10$ by $2$ and simplify.

Divide each term in $2 q \leq - 10$ by $2$ .

$\frac{2 q}{2} \leq \frac{- 10}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 q}{2} \leq \frac{- 10}{2}$

Divide $q$ by $1$ .

$q \leq \frac{- 10}{2}$

Simplify the right side.

Divide $- 10$ by $2$ .

$q \leq - 5$

The result can be shown in multiple forms.

Inequality Form:

$q \leq - 5$

Interval Notation:

$(- \infty, - 5]$