Algebra Examples

$- 16 < 6 k + 2 < 0$

Step 1

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

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Step 1.1

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

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

Step 1.2

Subtract $2$ from $- 16$ .

$- 18 < 6 k < 0 - 2$

Step 1.3

Subtract $2$ from $0$ .

$- 18 < 6 k < - 2$

Step 2

Divide each term in the inequality by $6$ .

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

Step 3

Divide $- 18$ by $6$ .

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

Step 4

Cancel the common factor of $6$ .

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Step 4.1

Cancel the common factor.

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

Step 4.2

Divide $k$ by $1$ .

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

Step 5

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

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Step 5.1

Factor $2$ out of $- 2$ .

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

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $2$ out of $6$ .

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

Step 5.2.2

Cancel the common factor.

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

Step 5.2.3

Rewrite the expression.

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

Step 6

Move the negative in front of the fraction.

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

Step 7

The result can be shown in multiple forms.

Inequality Form:

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

Interval Notation:

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

Step 8