Algebra Examples

$\frac{8}{11} (n - 10) = 64$

Step 1

Multiply both sides of the equation by $\frac{11}{8}$ .

$\frac{11}{8} (\frac{8}{11} \cdot (n - 10)) = \frac{11}{8} \cdot 64$

Step 2

Simplify both sides of the equation.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $\frac{11}{8} (\frac{8}{11} \cdot (n - 10))$ .

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Step 2.1.1.1

Apply the distributive property.

$\frac{11}{8} (\frac{8}{11} n + \frac{8}{11} \cdot - 10) = \frac{11}{8} \cdot 64$

Step 2.1.1.2

Combine $\frac{8}{11}$ and $n$ .

$\frac{11}{8} (\frac{8 n}{11} + \frac{8}{11} \cdot - 10) = \frac{11}{8} \cdot 64$

Step 2.1.1.3

Multiply $\frac{8}{11} \cdot - 10$ .

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Step 2.1.1.3.1

Combine $\frac{8}{11}$ and $- 10$ .

$\frac{11}{8} (\frac{8 n}{11} + \frac{8 \cdot - 10}{11}) = \frac{11}{8} \cdot 64$

Step 2.1.1.3.2

Multiply $8$ by $- 10$ .

$\frac{11}{8} (\frac{8 n}{11} + \frac{- 80}{11}) = \frac{11}{8} \cdot 64$

Step 2.1.1.4

Move the negative in front of the fraction.

$\frac{11}{8} (\frac{8 n}{11} - \frac{80}{11}) = \frac{11}{8} \cdot 64$

Step 2.1.1.5

Apply the distributive property.

$\frac{11}{8} \cdot \frac{8 n}{11} + \frac{11}{8} (- \frac{80}{11}) = \frac{11}{8} \cdot 64$

Step 2.1.1.6

Cancel the common factor of $11$ .

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Step 2.1.1.6.1

Cancel the common factor.

$\frac{11}{8} \cdot \frac{8 n}{11} + \frac{11}{8} (- \frac{80}{11}) = \frac{11}{8} \cdot 64$

Step 2.1.1.6.2

Rewrite the expression.

$\frac{1}{8} (8 n) + \frac{11}{8} (- \frac{80}{11}) = \frac{11}{8} \cdot 64$

Step 2.1.1.7

Cancel the common factor of $8$ .

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Step 2.1.1.7.1

Factor $8$ out of $8 n$ .

$\frac{1}{8} (8 (n)) + \frac{11}{8} (- \frac{80}{11}) = \frac{11}{8} \cdot 64$

Step 2.1.1.7.2

Cancel the common factor.

$\frac{1}{8} (8 n) + \frac{11}{8} (- \frac{80}{11}) = \frac{11}{8} \cdot 64$

Step 2.1.1.7.3

Rewrite the expression.

$n + \frac{11}{8} (- \frac{80}{11}) = \frac{11}{8} \cdot 64$

Step 2.1.1.8

Cancel the common factor of $11$ .

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Step 2.1.1.8.1

Move the leading negative in $- \frac{80}{11}$ into the numerator.

$n + \frac{11}{8} \cdot \frac{- 80}{11} = \frac{11}{8} \cdot 64$

Step 2.1.1.8.2

Cancel the common factor.

$n + \frac{11}{8} \cdot \frac{- 80}{11} = \frac{11}{8} \cdot 64$

Step 2.1.1.8.3

Rewrite the expression.

$n + \frac{1}{8} \cdot - 80 = \frac{11}{8} \cdot 64$

Step 2.1.1.9

Cancel the common factor of $8$ .

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Step 2.1.1.9.1

Factor $8$ out of $- 80$ .

$n + \frac{1}{8} \cdot (8 (- 10)) = \frac{11}{8} \cdot 64$

Step 2.1.1.9.2

Cancel the common factor.

$n + \frac{1}{8} \cdot (8 \cdot - 10) = \frac{11}{8} \cdot 64$

Step 2.1.1.9.3

Rewrite the expression.

$n - 10 = \frac{11}{8} \cdot 64$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $\frac{11}{8} \cdot 64$ .

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Step 2.2.1.1

Cancel the common factor of $8$ .

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Step 2.2.1.1.1

Factor $8$ out of $64$ .

$n - 10 = \frac{11}{8} \cdot (8 (8))$

Step 2.2.1.1.2

Cancel the common factor.

$n - 10 = \frac{11}{8} \cdot (8 \cdot 8)$

Step 2.2.1.1.3

Rewrite the expression.

$n - 10 = 11 \cdot 8$

Step 2.2.1.2

Multiply $11$ by $8$ .

$n - 10 = 88$

Step 3

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

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Step 3.1

Add $10$ to both sides of the equation.

$n = 88 + 10$

Step 3.2

Add $88$ and $10$ .

$n = 98$