Basic Math Examples

$- \frac{3}{8} n - 11 = 4$

Step 1

Simplify each term.

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Step 1.1

Combine $n$ and $\frac{3}{8}$ .

$- \frac{n \cdot 3}{8} - 11 = 4$

Step 1.2

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

$- \frac{3 n}{8} - 11 = 4$

Step 2

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

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Step 2.1

Add $11$ to both sides of the equation.

$- \frac{3 n}{8} = 4 + 11$

Step 2.2

Add $4$ and $11$ .

$- \frac{3 n}{8} = 15$

Step 3

Multiply both sides of the equation by $- \frac{8}{3}$ .

$- \frac{8}{3} (- \frac{3 n}{8}) = - \frac{8}{3} \cdot 15$

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

Simplify $- \frac{8}{3} (- \frac{3 n}{8})$ .

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Step 4.1.1.1

Cancel the common factor of $8$ .

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Step 4.1.1.1.1

Move the leading negative in $- \frac{8}{3}$ into the numerator.

$\frac{- 8}{3} (- \frac{3 n}{8}) = - \frac{8}{3} \cdot 15$

Step 4.1.1.1.2

Move the leading negative in $- \frac{3 n}{8}$ into the numerator.

$\frac{- 8}{3} \cdot \frac{- 3 n}{8} = - \frac{8}{3} \cdot 15$

Step 4.1.1.1.3

Factor $8$ out of $- 8$ .

$\frac{8 (- 1)}{3} \cdot \frac{- 3 n}{8} = - \frac{8}{3} \cdot 15$

Step 4.1.1.1.4

Cancel the common factor.

$\frac{8 \cdot - 1}{3} \cdot \frac{- 3 n}{8} = - \frac{8}{3} \cdot 15$

Step 4.1.1.1.5

Rewrite the expression.

$\frac{- 1}{3} (- 3 n) = - \frac{8}{3} \cdot 15$

Step 4.1.1.2

Cancel the common factor of $3$ .

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Step 4.1.1.2.1

Factor $3$ out of $- 3 n$ .

$\frac{- 1}{3} (3 (- n)) = - \frac{8}{3} \cdot 15$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{- 1}{3} (3 (- n)) = - \frac{8}{3} \cdot 15$

Step 4.1.1.2.3

Rewrite the expression.

$- - n = - \frac{8}{3} \cdot 15$

Step 4.1.1.3

Multiply.

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Step 4.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 n = - \frac{8}{3} \cdot 15$

Step 4.1.1.3.2

Multiply $n$ by $1$ .

$n = - \frac{8}{3} \cdot 15$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $- \frac{8}{3} \cdot 15$ .

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Step 4.2.1.1

Cancel the common factor of $3$ .

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Step 4.2.1.1.1

Move the leading negative in $- \frac{8}{3}$ into the numerator.

$n = \frac{- 8}{3} \cdot 15$

Step 4.2.1.1.2

Factor $3$ out of $15$ .

$n = \frac{- 8}{3} \cdot (3 (5))$

Step 4.2.1.1.3

Cancel the common factor.

$n = \frac{- 8}{3} \cdot (3 \cdot 5)$

Step 4.2.1.1.4

Rewrite the expression.

$n = - 8 \cdot 5$

Step 4.2.1.2

Multiply $- 8$ by $5$ .

$n = - 40$