Trigonometry Examples

$\frac{5 k - 2}{- 5} > 2$

Step 1

Multiply both sides by $- 5$ .

$\frac{5 k - 2}{- 5} \cdot - 5 < 2 \cdot - 5$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $\frac{5 k - 2}{- 5} \cdot - 5$ .

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Step 2.1.1.1

Cancel the common factor of $5$ .

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Step 2.1.1.1.1

Factor $5$ out of $- 5$ .

$\frac{5 k - 2}{5 (- 1)} \cdot - 5 < 2 \cdot - 5$

Step 2.1.1.1.2

Factor $5$ out of $- 5$ .

$\frac{5 k - 2}{5 \cdot - 1} \cdot (5 \cdot - 1) < 2 \cdot - 5$

Step 2.1.1.1.3

Cancel the common factor.

$\frac{5 k - 2}{5 \cdot - 1} \cdot (5 \cdot - 1) < 2 \cdot - 5$

Step 2.1.1.1.4

Rewrite the expression.

$\frac{5 k - 2}{- 1} \cdot - 1 < 2 \cdot - 5$

Step 2.1.1.2

Combine $\frac{5 k - 2}{- 1}$ and $- 1$ .

$\frac{(5 k - 2) \cdot - 1}{- 1} < 2 \cdot - 5$

Step 2.1.1.3

Simplify the expression.

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Step 2.1.1.3.1

Move the negative one from the denominator of $\frac{(5 k - 2) \cdot - 1}{- 1}$ .

$- 1 \cdot ((5 k - 2) \cdot - 1) < 2 \cdot - 5$

Step 2.1.1.3.2

Rewrite $- 1 \cdot ((5 k - 2) \cdot - 1)$ as $- ((5 k - 2) \cdot - 1)$ .

$- ((5 k - 2) \cdot - 1) < 2 \cdot - 5$

Step 2.1.1.4

Apply the distributive property.

$- (5 k \cdot - 1 - 2 \cdot - 1) < 2 \cdot - 5$

Step 2.1.1.5

Multiply.

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Step 2.1.1.5.1

Multiply $- 1$ by $5$ .

$- (- 5 k - 2 \cdot - 1) < 2 \cdot - 5$

Step 2.1.1.5.2

Multiply $- 2$ by $- 1$ .

$- (- 5 k + 2) < 2 \cdot - 5$

Step 2.1.1.6

Apply the distributive property.

$- (- 5 k) - 1 \cdot 2 < 2 \cdot - 5$

Step 2.1.1.7

Multiply.

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Step 2.1.1.7.1

Multiply $- 5$ by $- 1$ .

$5 k - 1 \cdot 2 < 2 \cdot - 5$

Step 2.1.1.7.2

Multiply $- 1$ by $2$ .

$5 k - 2 < 2 \cdot - 5$

Step 2.2

Simplify the right side.

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Step 2.2.1

Multiply $2$ by $- 5$ .

$5 k - 2 < - 10$

Step 3

Solve for $k$ .

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Step 3.1

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

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Step 3.1.1

Add $2$ to both sides of the inequality.

$5 k < - 10 + 2$

Step 3.1.2

Add $- 10$ and $2$ .

$5 k < - 8$

Step 3.2

Divide each term in $5 k < - 8$ by $5$ and simplify.

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Step 3.2.1

Divide each term in $5 k < - 8$ by $5$ .

$\frac{5 k}{5} < \frac{- 8}{5}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $5$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{5 k}{5} < \frac{- 8}{5}$

Step 3.2.2.1.2

Divide $k$ by $1$ .

$k < \frac{- 8}{5}$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Move the negative in front of the fraction.

$k < - \frac{8}{5}$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$k < - \frac{8}{5}$

Interval Notation:

$(- \infty, - \frac{8}{5})$