Trigonometry Examples

$(3 n - 5) = - 10 (3 n - 5) + 35$

Step 1

Simplify $- 10 (3 n - 5) + 35$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$3 n - 5 = - 10 (3 n) - 10 \cdot - 5 + 35$

Step 1.1.2

Multiply $3$ by $- 10$ .

$3 n - 5 = - 30 n - 10 \cdot - 5 + 35$

Step 1.1.3

Multiply $- 10$ by $- 5$ .

$3 n - 5 = - 30 n + 50 + 35$

Step 1.2

Add $50$ and $35$ .

$3 n - 5 = - 30 n + 85$

Step 2

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

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Step 2.1

Add $30 n$ to both sides of the equation.

$3 n - 5 + 30 n = 85$

Step 2.2

Add $3 n$ and $30 n$ .

$33 n - 5 = 85$

Step 3

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

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Step 3.1

Add $5$ to both sides of the equation.

$33 n = 85 + 5$

Step 3.2

Add $85$ and $5$ .

$33 n = 90$

Step 4

Divide each term in $33 n = 90$ by $33$ and simplify.

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Step 4.1

Divide each term in $33 n = 90$ by $33$ .

$\frac{33 n}{33} = \frac{90}{33}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $33$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{33 n}{33} = \frac{90}{33}$

Step 4.2.1.2

Divide $n$ by $1$ .

$n = \frac{90}{33}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Cancel the common factor of $90$ and $33$ .

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Step 4.3.1.1

Factor $3$ out of $90$ .

$n = \frac{3 (30)}{33}$

Step 4.3.1.2

Cancel the common factors.

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Step 4.3.1.2.1

Factor $3$ out of $33$ .

$n = \frac{3 \cdot 30}{3 \cdot 11}$

Step 4.3.1.2.2

Cancel the common factor.

$n = \frac{3 \cdot 30}{3 \cdot 11}$

Step 4.3.1.2.3

Rewrite the expression.

$n = \frac{30}{11}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$n = \frac{30}{11}$

Decimal Form:

$n = 2.\overline{72}$

Mixed Number Form:

$n = 2 \frac{8}{11}$