Trigonometry Examples

$2 y - 7 = \frac{4}{3} y + 8$

Step 1

Combine $\frac{4}{3}$ and $y$ .

$2 y - 7 = \frac{4 y}{3} + 8$

Step 2

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

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Step 2.1

Subtract $\frac{4 y}{3}$ from both sides of the equation.

$2 y - 7 - \frac{4 y}{3} = 8$

Step 2.2

To write $2 y$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$2 y \cdot \frac{3}{3} - \frac{4 y}{3} - 7 = 8$

Step 2.3

Combine $2 y$ and $\frac{3}{3}$ .

$\frac{2 y \cdot 3}{3} - \frac{4 y}{3} - 7 = 8$

Step 2.4

Combine the numerators over the common denominator.

$\frac{2 y \cdot 3 - 4 y}{3} - 7 = 8$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Factor $2 y$ out of $2 y \cdot 3 - 4 y$ .

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Step 2.5.1.1

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

$\frac{2 y (3) - 4 y}{3} - 7 = 8$

Step 2.5.1.2

Factor $2 y$ out of $- 4 y$ .

$\frac{2 y (3) + 2 y (- 2)}{3} - 7 = 8$

Step 2.5.1.3

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

$\frac{2 y (3 - 2)}{3} - 7 = 8$

Step 2.5.2

Subtract $2$ from $3$ .

$\frac{2 y \cdot 1}{3} - 7 = 8$

Step 2.5.3

Multiply $2$ by $1$ .

$\frac{2 y}{3} - 7 = 8$

Step 3

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

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Step 3.1

Add $7$ to both sides of the equation.

$\frac{2 y}{3} = 8 + 7$

Step 3.2

Add $8$ and $7$ .

$\frac{2 y}{3} = 15$

Step 4

Multiply both sides of the equation by $\frac{3}{2}$ .

$\frac{3}{2} \cdot \frac{2 y}{3} = \frac{3}{2} \cdot 15$

Step 5

Simplify both sides of the equation.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Simplify $\frac{3}{2} \cdot \frac{2 y}{3}$ .

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Step 5.1.1.1

Cancel the common factor of $3$ .

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Step 5.1.1.1.1

Cancel the common factor.

$\frac{3}{2} \cdot \frac{2 y}{3} = \frac{3}{2} \cdot 15$

Step 5.1.1.1.2

Rewrite the expression.

$\frac{1}{2} (2 y) = \frac{3}{2} \cdot 15$

Step 5.1.1.2

Cancel the common factor of $2$ .

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Step 5.1.1.2.1

Factor $2$ out of $2 y$ .

$\frac{1}{2} (2 (y)) = \frac{3}{2} \cdot 15$

Step 5.1.1.2.2

Cancel the common factor.

$\frac{1}{2} (2 y) = \frac{3}{2} \cdot 15$

Step 5.1.1.2.3

Rewrite the expression.

$y = \frac{3}{2} \cdot 15$

Step 5.2

Simplify the right side.

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Step 5.2.1

Multiply $\frac{3}{2} \cdot 15$ .

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Step 5.2.1.1

Combine $\frac{3}{2}$ and $15$ .

$y = \frac{3 \cdot 15}{2}$

Step 5.2.1.2

Multiply $3$ by $15$ .

$y = \frac{45}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$y = \frac{45}{2}$

Decimal Form:

$y = 22.5$

Mixed Number Form:

$y = 22 \frac{1}{2}$