Trigonometry Examples

$3 y + 3 > \frac{2}{9} y - 5$

Step 1

Combine $\frac{2}{9}$ and $y$ .

$3 y + 3 > \frac{2 y}{9} - 5$

Step 2

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

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Step 2.1

Subtract $\frac{2 y}{9}$ from both sides of the inequality.

$3 y + 3 - \frac{2 y}{9} > - 5$

Step 2.2

To write $3 y$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$3 y \cdot \frac{9}{9} - \frac{2 y}{9} + 3 > - 5$

Step 2.3

Combine $3 y$ and $\frac{9}{9}$ .

$\frac{3 y \cdot 9}{9} - \frac{2 y}{9} + 3 > - 5$

Step 2.4

Combine the numerators over the common denominator.

$\frac{3 y \cdot 9 - 2 y}{9} + 3 > - 5$

Step 2.5

Simplify each term.

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Step 2.5.1

Simplify the numerator.

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Step 2.5.1.1

Factor $y$ out of $3 y \cdot 9 - 2 y$ .

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Step 2.5.1.1.1

Factor $y$ out of $3 y \cdot 9$ .

$\frac{y (3 \cdot 9) - 2 y}{9} + 3 > - 5$

Step 2.5.1.1.2

Factor $y$ out of $- 2 y$ .

$\frac{y (3 \cdot 9) + y \cdot - 2}{9} + 3 > - 5$

Step 2.5.1.1.3

Factor $y$ out of $y (3 \cdot 9) + y \cdot - 2$ .

$\frac{y (3 \cdot 9 - 2)}{9} + 3 > - 5$

Step 2.5.1.2

Multiply $3$ by $9$ .

$\frac{y (27 - 2)}{9} + 3 > - 5$

Step 2.5.1.3

Subtract $2$ from $27$ .

$\frac{y \cdot 25}{9} + 3 > - 5$

Step 2.5.2

Move $25$ to the left of $y$ .

$\frac{25 y}{9} + 3 > - 5$

Step 3

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

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Step 3.1

Subtract $3$ from both sides of the inequality.

$\frac{25 y}{9} > - 5 - 3$

Step 3.2

Subtract $3$ from $- 5$ .

$\frac{25 y}{9} > - 8$

Step 4

Multiply both sides by $9$ .

$\frac{25 y}{9} \cdot 9 > - 8 \cdot 9$

Step 5

Simplify.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Cancel the common factor of $9$ .

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Step 5.1.1.1

Cancel the common factor.

$\frac{25 y}{9} \cdot 9 > - 8 \cdot 9$

Step 5.1.1.2

Rewrite the expression.

$25 y > - 8 \cdot 9$

Step 5.2

Simplify the right side.

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Step 5.2.1

Multiply $- 8$ by $9$ .

$25 y > - 72$

Step 6

Divide each term in $25 y > - 72$ by $25$ and simplify.

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Step 6.1

Divide each term in $25 y > - 72$ by $25$ .

$\frac{25 y}{25} > \frac{- 72}{25}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $25$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{25 y}{25} > \frac{- 72}{25}$

Step 6.2.1.2

Divide $y$ by $1$ .

$y > \frac{- 72}{25}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Move the negative in front of the fraction.

$y > - \frac{72}{25}$

Step 7

Convert the inequality to interval notation.

$(- \frac{72}{25}, \infty)$

Step 8