Algebra Examples

$\frac{1}{3} (2 n - \frac{1}{4}) = \frac{7}{12}$

Step 1

Multiply both sides of the equation by $3$ .

$3 (\frac{1}{3} \cdot (2 n - \frac{1}{4})) = 3 (\frac{7}{12})$

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 $3 (\frac{1}{3} \cdot (2 n - \frac{1}{4}))$ .

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Step 2.1.1.1

Apply the distributive property.

$3 (\frac{1}{3} (2 n) + \frac{1}{3} (- \frac{1}{4})) = 3 (\frac{7}{12})$

Step 2.1.1.2

Multiply $\frac{1}{3} (2 n)$ .

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Step 2.1.1.2.1

Combine $2$ and $\frac{1}{3}$ .

$3 (\frac{2}{3} n + \frac{1}{3} (- \frac{1}{4})) = 3 (\frac{7}{12})$

Step 2.1.1.2.2

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

$3 (\frac{2 n}{3} + \frac{1}{3} (- \frac{1}{4})) = 3 (\frac{7}{12})$

Step 2.1.1.3

Multiply $\frac{1}{3} (- \frac{1}{4})$ .

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Step 2.1.1.3.1

Multiply $\frac{1}{3}$ by $\frac{1}{4}$ .

$3 (\frac{2 n}{3} - \frac{1}{3 \cdot 4}) = 3 (\frac{7}{12})$

Step 2.1.1.3.2

Multiply $3$ by $4$ .

$3 (\frac{2 n}{3} - \frac{1}{12}) = 3 (\frac{7}{12})$

Step 2.1.1.4

Apply the distributive property.

$3 \frac{2 n}{3} + 3 (- \frac{1}{12}) = 3 (\frac{7}{12})$

Step 2.1.1.5

Cancel the common factor of $3$ .

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Step 2.1.1.5.1

Cancel the common factor.

$3 \frac{2 n}{3} + 3 (- \frac{1}{12}) = 3 (\frac{7}{12})$

Step 2.1.1.5.2

Rewrite the expression.

$2 n + 3 (- \frac{1}{12}) = 3 (\frac{7}{12})$

Step 2.1.1.6

Cancel the common factor of $3$ .

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Step 2.1.1.6.1

Move the leading negative in $- \frac{1}{12}$ into the numerator.

$2 n + 3 (\frac{- 1}{12}) = 3 (\frac{7}{12})$

Step 2.1.1.6.2

Factor $3$ out of $12$ .

$2 n + 3 \frac{- 1}{3 (4)} = 3 (\frac{7}{12})$

Step 2.1.1.6.3

Cancel the common factor.

$2 n + 3 \frac{- 1}{3 \cdot 4} = 3 (\frac{7}{12})$

Step 2.1.1.6.4

Rewrite the expression.

$2 n + \frac{- 1}{4} = 3 (\frac{7}{12})$

Step 2.1.1.7

Move the negative in front of the fraction.

$2 n - \frac{1}{4} = 3 (\frac{7}{12})$

Step 2.2

Simplify the right side.

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Step 2.2.1

Cancel the common factor of $3$ .

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Step 2.2.1.1

Factor $3$ out of $12$ .

$2 n - \frac{1}{4} = 3 \frac{7}{3 (4)}$

Step 2.2.1.2

Cancel the common factor.

$2 n - \frac{1}{4} = 3 \frac{7}{3 \cdot 4}$

Step 2.2.1.3

Rewrite the expression.

$2 n - \frac{1}{4} = \frac{7}{4}$

Step 3

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

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Step 3.1

Add $\frac{1}{4}$ to both sides of the equation.

$2 n = \frac{7}{4} + \frac{1}{4}$

Step 3.2

Combine the numerators over the common denominator.

$2 n = \frac{7 + 1}{4}$

Step 3.3

Add $7$ and $1$ .

$2 n = \frac{8}{4}$

Step 3.4

Divide $8$ by $4$ .

$2 n = 2$

Step 4

Divide each term in $2 n = 2$ by $2$ and simplify.

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Step 4.1

Divide each term in $2 n = 2$ by $2$ .

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

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $2$ .

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Step 4.2.1.1

Cancel the common factor.

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

Step 4.2.1.2

Divide $n$ by $1$ .

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

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $2$ by $2$ .

$n = 1$