Algebra Examples

$- 20 < - 5 k - 15 < 5$

Step 1

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

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Step 1.1

Add $15$ to each section of the inequality because it does not contain the variable we are trying to solve for.

$- 20 + 15 < - 5 k < 5 + 15$

Step 1.2

Add $- 20$ and $15$ .

$- 5 < - 5 k < 5 + 15$

Step 1.3

Add $5$ and $15$ .

$- 5 < - 5 k < 20$

Step 2

Divide each term in the inequality by $- 5$ .

$\frac{- 5}{- 5} > \frac{- 5 k}{- 5} > \frac{20}{- 5}$

Step 3

Divide $- 5$ by $- 5$ .

$1 > \frac{- 5 k}{- 5} > \frac{20}{- 5}$

Step 4

Cancel the common factor of $- 5$ .

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Step 4.1

Cancel the common factor.

$1 > \frac{- 5 k}{- 5} > \frac{20}{- 5}$

Step 4.2

Divide $k$ by $1$ .

$1 > k > \frac{20}{- 5}$

Step 5

Divide $20$ by $- 5$ .

$1 > k > - 4$

Step 6

Rewrite the interval so that the left value is less than the right value. This is the correct way to write an interval solution.

$- 4 < k < 1$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$- 4 < k < 1$

Interval Notation:

$(- 4, 1)$

Step 8