Basic Math Examples

$\frac{6}{5} \cdot (n - 2) + 7 = 9$

Step 1

Simplify $\frac{6}{5} \cdot (n - 2) + 7$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$\frac{6}{5} n + \frac{6}{5} \cdot - 2 + 7 = 9$

Step 1.1.2

Combine $\frac{6}{5}$ and $n$ .

$\frac{6 n}{5} + \frac{6}{5} \cdot - 2 + 7 = 9$

Step 1.1.3

Multiply $\frac{6}{5} \cdot - 2$ .

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Step 1.1.3.1

Combine $\frac{6}{5}$ and $- 2$ .

$\frac{6 n}{5} + \frac{6 \cdot - 2}{5} + 7 = 9$

Step 1.1.3.2

Multiply $6$ by $- 2$ .

$\frac{6 n}{5} + \frac{- 12}{5} + 7 = 9$

Step 1.1.4

Move the negative in front of the fraction.

$\frac{6 n}{5} - \frac{12}{5} + 7 = 9$

Step 1.2

To write $7$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{6 n}{5} - \frac{12}{5} + 7 \cdot \frac{5}{5} = 9$

Step 1.3

Combine $7$ and $\frac{5}{5}$ .

$\frac{6 n}{5} - \frac{12}{5} + \frac{7 \cdot 5}{5} = 9$

Step 1.4

Combine the numerators over the common denominator.

$\frac{6 n}{5} + \frac{- 12 + 7 \cdot 5}{5} = 9$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Multiply $7$ by $5$ .

$\frac{6 n}{5} + \frac{- 12 + 35}{5} = 9$

Step 1.5.2

Add $- 12$ and $35$ .

$\frac{6 n}{5} + \frac{23}{5} = 9$

Step 2

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

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Step 2.1

Subtract $\frac{23}{5}$ from both sides of the equation.

$\frac{6 n}{5} = 9 - \frac{23}{5}$

Step 2.2

To write $9$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{6 n}{5} = 9 \cdot \frac{5}{5} - \frac{23}{5}$

Step 2.3

Combine $9$ and $\frac{5}{5}$ .

$\frac{6 n}{5} = \frac{9 \cdot 5}{5} - \frac{23}{5}$

Step 2.4

Combine the numerators over the common denominator.

$\frac{6 n}{5} = \frac{9 \cdot 5 - 23}{5}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $9$ by $5$ .

$\frac{6 n}{5} = \frac{45 - 23}{5}$

Step 2.5.2

Subtract $23$ from $45$ .

$\frac{6 n}{5} = \frac{22}{5}$

Step 3

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$6 n = 22$

Step 4

Divide each term in $6 n = 22$ by $6$ and simplify.

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Step 4.1

Divide each term in $6 n = 22$ by $6$ .

$\frac{6 n}{6} = \frac{22}{6}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $6$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{6 n}{6} = \frac{22}{6}$

Step 4.2.1.2

Divide $n$ by $1$ .

$n = \frac{22}{6}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Cancel the common factor of $22$ and $6$ .

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Step 4.3.1.1

Factor $2$ out of $22$ .

$n = \frac{2 (11)}{6}$

Step 4.3.1.2

Cancel the common factors.

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Step 4.3.1.2.1

Factor $2$ out of $6$ .

$n = \frac{2 \cdot 11}{2 \cdot 3}$

Step 4.3.1.2.2

Cancel the common factor.

$n = \frac{2 \cdot 11}{2 \cdot 3}$

Step 4.3.1.2.3

Rewrite the expression.

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$n = 3.\overline{6}$

Mixed Number Form:

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