Finite Math Examples

$- 11 < 5 k + 4 < 39$

Step 1

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

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Step 1.1

Subtract $4$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$- 11 - 4 < 5 k < 39 - 4$

Step 1.2

Subtract $4$ from $- 11$ .

$- 15 < 5 k < 39 - 4$

Step 1.3

Subtract $4$ from $39$ .

$- 15 < 5 k < 35$

Step 2

Divide each term in the inequality by $5$ .

$\frac{- 15}{5} < \frac{5 k}{5} < \frac{35}{5}$

Step 3

Divide $- 15$ by $5$ .

$- 3 < \frac{5 k}{5} < \frac{35}{5}$

Step 4

Cancel the common factor of $5$ .

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Step 4.1

Cancel the common factor.

$- 3 < \frac{5 k}{5} < \frac{35}{5}$

Step 4.2

Divide $k$ by $1$ .

$- 3 < k < \frac{35}{5}$

Step 5

Divide $35$ by $5$ .

$- 3 < k < 7$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$- 3 < k < 7$

Interval Notation:

$(- 3, 7)$

Step 7