Algebra Examples

$- 8 \leq \frac{2}{5} (k - 2)$

Step 1

Rewrite so $k$ is on the left side of the inequality.

$\frac{2}{5} \cdot (k - 2) \geq - 8$

Step 2

Multiply each term in $\frac{2}{5} \cdot (k - 2) \geq - 8$ by $\frac{5}{2}$ to eliminate the fractions.

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Step 2.1

Multiply each term in $\frac{2}{5} \cdot (k - 2) \geq - 8$ by $\frac{5}{2}$ .

$\frac{2}{5} \cdot (k - 2) \frac{5}{2} \geq - 8 (\frac{5}{2})$

Step 2.2

Simplify the left side.

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Step 2.2.1

Apply the distributive property.

$(\frac{2}{5} k + \frac{2}{5} \cdot - 2) \frac{5}{2} \geq - 8 (\frac{5}{2})$

Step 2.2.2

Combine $\frac{2}{5}$ and $k$ .

$(\frac{2 k}{5} + \frac{2}{5} \cdot - 2) \frac{5}{2} \geq - 8 (\frac{5}{2})$

Step 2.2.3

Multiply $\frac{2}{5} \cdot - 2$ .

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Step 2.2.3.1

Combine $\frac{2}{5}$ and $- 2$ .

$(\frac{2 k}{5} + \frac{2 \cdot - 2}{5}) \frac{5}{2} \geq - 8 (\frac{5}{2})$

Step 2.2.3.2

Multiply $2$ by $- 2$ .

$(\frac{2 k}{5} + \frac{- 4}{5}) \frac{5}{2} \geq - 8 (\frac{5}{2})$

Step 2.2.4

Move the negative in front of the fraction.

$(\frac{2 k}{5} - \frac{4}{5}) \frac{5}{2} \geq - 8 (\frac{5}{2})$

Step 2.2.5

Apply the distributive property.

$\frac{2 k}{5} \cdot \frac{5}{2} - \frac{4}{5} \cdot \frac{5}{2} \geq - 8 (\frac{5}{2})$

Step 2.2.6

Cancel the common factor of $2$ .

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Step 2.2.6.1

Factor $2$ out of $2 k$ .

$\frac{2 (k)}{5} \cdot \frac{5}{2} - \frac{4}{5} \cdot \frac{5}{2} \geq - 8 (\frac{5}{2})$

Step 2.2.6.2

Cancel the common factor.

$\frac{2 k}{5} \cdot \frac{5}{2} - \frac{4}{5} \cdot \frac{5}{2} \geq - 8 (\frac{5}{2})$

Step 2.2.6.3

Rewrite the expression.

$\frac{k}{5} \cdot 5 - \frac{4}{5} \cdot \frac{5}{2} \geq - 8 (\frac{5}{2})$

Step 2.2.7

Cancel the common factor of $5$ .

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Step 2.2.7.1

Cancel the common factor.

$\frac{k}{5} \cdot 5 - \frac{4}{5} \cdot \frac{5}{2} \geq - 8 (\frac{5}{2})$

Step 2.2.7.2

Rewrite the expression.

$k - \frac{4}{5} \cdot \frac{5}{2} \geq - 8 (\frac{5}{2})$

Step 2.2.8

Cancel the common factor of $2$ .

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Step 2.2.8.1

Move the leading negative in $- \frac{4}{5}$ into the numerator.

$k + \frac{- 4}{5} \cdot \frac{5}{2} \geq - 8 (\frac{5}{2})$

Step 2.2.8.2

Factor $2$ out of $- 4$ .

$k + \frac{2 (- 2)}{5} \cdot \frac{5}{2} \geq - 8 (\frac{5}{2})$

Step 2.2.8.3

Cancel the common factor.

$k + \frac{2 \cdot - 2}{5} \cdot \frac{5}{2} \geq - 8 (\frac{5}{2})$

Step 2.2.8.4

Rewrite the expression.

$k + \frac{- 2}{5} \cdot 5 \geq - 8 (\frac{5}{2})$

Step 2.2.9

Cancel the common factor of $5$ .

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Step 2.2.9.1

Cancel the common factor.

$k + \frac{- 2}{5} \cdot 5 \geq - 8 (\frac{5}{2})$

Step 2.2.9.2

Rewrite the expression.

$k - 2 \geq - 8 (\frac{5}{2})$

Step 2.3

Simplify the right side.

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Step 2.3.1

Cancel the common factor of $2$ .

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Step 2.3.1.1

Factor $2$ out of $- 8$ .

$k - 2 \geq 2 (- 4) \frac{5}{2}$

Step 2.3.1.2

Cancel the common factor.

$k - 2 \geq 2 \cdot - 4 \frac{5}{2}$

Step 2.3.1.3

Rewrite the expression.

$k - 2 \geq - 4 \cdot 5$

Step 2.3.2

Multiply $- 4$ by $5$ .

$k - 2 \geq - 20$

Step 3

Move all terms not containing $k$ to the right side of the inequality.

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Step 3.1

Add $2$ to both sides of the inequality.

$k \geq - 20 + 2$

Step 3.2

Add $- 20$ and $2$ .

$k \geq - 18$

Step 4