Basic Math Examples

$n = \frac{2}{3} n - 10$

Step 1

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

$n = \frac{2 n}{3} - 10$

Step 2

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

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Step 2.1

Subtract $\frac{2 n}{3}$ from both sides of the equation.

$n - \frac{2 n}{3} = - 10$

Step 2.2

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

$n \cdot \frac{3}{3} - \frac{2 n}{3} = - 10$

Step 2.3

Combine $n$ and $\frac{3}{3}$ .

$\frac{n \cdot 3}{3} - \frac{2 n}{3} = - 10$

Step 2.4

Combine the numerators over the common denominator.

$\frac{n \cdot 3 - 2 n}{3} = - 10$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Move $3$ to the left of $n$ .

$\frac{3 \cdot n - 2 n}{3} = - 10$

Step 2.5.2

Subtract $2 n$ from $3 n$ .

$\frac{n}{3} = - 10$

Step 3

Multiply both sides of the equation by $3$ .

$3 \frac{n}{3} = 3 \cdot - 10$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Cancel the common factor of $3$ .

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Step 4.1.1.1

Cancel the common factor.

$3 \frac{n}{3} = 3 \cdot - 10$

Step 4.1.1.2

Rewrite the expression.

$n = 3 \cdot - 10$

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $3$ by $- 10$ .

$n = - 30$