Trigonometry Examples

$- 30 r - 45 \leq - 5 (5 r + 11)$

Step 1

Simplify $- 5 (5 r + 11)$ .

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Step 1.1

Rewrite.

$- 30 r - 45 \leq 0 + 0 - 5 (5 r + 11)$

Step 1.2

Simplify by adding zeros.

$- 30 r - 45 \leq - 5 (5 r + 11)$

Step 1.3

Apply the distributive property.

$- 30 r - 45 \leq - 5 (5 r) - 5 \cdot 11$

Step 1.4

Multiply.

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Step 1.4.1

Multiply $5$ by $- 5$ .

$- 30 r - 45 \leq - 25 r - 5 \cdot 11$

Step 1.4.2

Multiply $- 5$ by $11$ .

$- 30 r - 45 \leq - 25 r - 55$

Step 2

Move all terms containing $r$ to the left side of the inequality.

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Step 2.1

Add $25 r$ to both sides of the inequality.

$- 30 r - 45 + 25 r \leq - 55$

Step 2.2

Add $- 30 r$ and $25 r$ .

$- 5 r - 45 \leq - 55$

Step 3

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

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Step 3.1

Add $45$ to both sides of the inequality.

$- 5 r \leq - 55 + 45$

Step 3.2

Add $- 55$ and $45$ .

$- 5 r \leq - 10$

Step 4

Divide each term in $- 5 r \leq - 10$ by $- 5$ and simplify.

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Step 4.1

Divide each term in $- 5 r \leq - 10$ by $- 5$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 5 r}{- 5} \geq \frac{- 10}{- 5}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $- 5$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{- 5 r}{- 5} \geq \frac{- 10}{- 5}$

Step 4.2.1.2

Divide $r$ by $1$ .

$r \geq \frac{- 10}{- 5}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $- 10$ by $- 5$ .

$r \geq 2$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$r \geq 2$

Interval Notation:

$[2, \infty)$