Solve the Inequality for k -16<6k+2<0

$- 16 < 6 k + 2 < 0$

Move all terms not containing $k$ from the center section of the inequality.

Subtract $2$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$- 16 - 2 < 6 k < 0 - 2$

Subtract $2$ from $- 16$ .

$- 18 < 6 k < 0 - 2$

Subtract $2$ from $0$ .

$- 18 < 6 k < - 2$

Divide each term in the inequality by $6$ .

$\frac{- 18}{6} < \frac{6 k}{6} < \frac{- 2}{6}$

Divide $- 18$ by $6$ .

$- 3 < \frac{6 k}{6} < \frac{- 2}{6}$

Cancel the common factor of $6$ .

Cancel the common factor.

$- 3 < \frac{6 k}{6} < \frac{- 2}{6}$

Divide $k$ by $1$ .

$- 3 < k < \frac{- 2}{6}$

Cancel the common factor of $- 2$ and $6$ .

Factor $2$ out of $- 2$ .

$- 3 < k < \frac{2 (- 1)}{6}$

Cancel the common factors.

Factor $2$ out of $6$ .

$- 3 < k < \frac{2 \cdot - 1}{2 \cdot 3}$

Cancel the common factor.

$- 3 < k < \frac{2 \cdot - 1}{2 \cdot 3}$

Rewrite the expression.

$- 3 < k < \frac{- 1}{3}$

Move the negative in front of the fraction.

$- 3 < k < - \frac{1}{3}$

The result can be shown in multiple forms.

Inequality Form:

$- 3 < k < - \frac{1}{3}$

Interval Notation:

$(- 3, - \frac{1}{3})$