Trigonometry Examples

$5 (2 g - 8) = 7$

Step 1

Divide each term in $5 (2 g - 8) = 7$ by $5$ and simplify.

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Step 1.1

Divide each term in $5 (2 g - 8) = 7$ by $5$ .

$\frac{5 (2 g - 8)}{5} = \frac{7}{5}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $5$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{5 (2 g - 8)}{5} = \frac{7}{5}$

Step 1.2.1.2

Divide $2 g - 8$ by $1$ .

$2 g - 8 = \frac{7}{5}$

Step 2

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

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Step 2.1

Add $8$ to both sides of the equation.

$2 g = \frac{7}{5} + 8$

Step 2.2

To write $8$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$2 g = \frac{7}{5} + 8 \cdot \frac{5}{5}$

Step 2.3

Combine $8$ and $\frac{5}{5}$ .

$2 g = \frac{7}{5} + \frac{8 \cdot 5}{5}$

Step 2.4

Combine the numerators over the common denominator.

$2 g = \frac{7 + 8 \cdot 5}{5}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $8$ by $5$ .

$2 g = \frac{7 + 40}{5}$

Step 2.5.2

Add $7$ and $40$ .

$2 g = \frac{47}{5}$

Step 3

Divide each term in $2 g = \frac{47}{5}$ by $2$ and simplify.

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Step 3.1

Divide each term in $2 g = \frac{47}{5}$ by $2$ .

$\frac{2 g}{2} = \frac{\frac{47}{5}}{2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $2$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{2 g}{2} = \frac{\frac{47}{5}}{2}$

Step 3.2.1.2

Divide $g$ by $1$ .

$g = \frac{\frac{47}{5}}{2}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Multiply the numerator by the reciprocal of the denominator.

$g = \frac{47}{5} \cdot \frac{1}{2}$

Step 3.3.2

Multiply $\frac{47}{5} \cdot \frac{1}{2}$ .

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Step 3.3.2.1

Multiply $\frac{47}{5}$ by $\frac{1}{2}$ .

$g = \frac{47}{5 \cdot 2}$

Step 3.3.2.2

Multiply $5$ by $2$ .

$g = \frac{47}{10}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$g = \frac{47}{10}$

Decimal Form:

$g = 4.7$

Mixed Number Form:

$g = 4 \frac{7}{10}$