Algebra Examples

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

Step 1

Multiply both sides of the equation by $\frac{2}{3}$ .

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

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 $\frac{2}{3} (\frac{3}{2} \cdot (\frac{7}{3} n + 1))$ .

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Step 2.1.1.1

Combine $\frac{7}{3}$ and $n$ .

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

Step 2.1.1.2

Apply the distributive property.

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

Step 2.1.1.3

Cancel the common factor of $3$ .

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Step 2.1.1.3.1

Cancel the common factor.

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

Step 2.1.1.3.2

Rewrite the expression.

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

Step 2.1.1.4

Combine $7$ and $\frac{1}{2}$ .

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

Step 2.1.1.5

Combine $\frac{7}{2}$ and $n$ .

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

Step 2.1.1.6

Multiply $\frac{3}{2}$ by $1$ .

$\frac{2}{3} (\frac{7 n}{2} + \frac{3}{2}) = \frac{2}{3} \cdot \frac{3}{2}$

Step 2.1.1.7

Apply the distributive property.

$\frac{2}{3} \cdot \frac{7 n}{2} + \frac{2}{3} \cdot \frac{3}{2} = \frac{2}{3} \cdot \frac{3}{2}$

Step 2.1.1.8

Cancel the common factor of $2$ .

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Step 2.1.1.8.1

Cancel the common factor.

$\frac{2}{3} \cdot \frac{7 n}{2} + \frac{2}{3} \cdot \frac{3}{2} = \frac{2}{3} \cdot \frac{3}{2}$

Step 2.1.1.8.2

Rewrite the expression.

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

Step 2.1.1.9

Combine $7$ and $\frac{1}{3}$ .

$\frac{7}{3} n + \frac{2}{3} \cdot \frac{3}{2} = \frac{2}{3} \cdot \frac{3}{2}$

Step 2.1.1.10

Combine $\frac{7}{3}$ and $n$ .

$\frac{7 n}{3} + \frac{2}{3} \cdot \frac{3}{2} = \frac{2}{3} \cdot \frac{3}{2}$

Step 2.1.1.11

Cancel the common factor of $2$ .

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Step 2.1.1.11.1

Cancel the common factor.

$\frac{7 n}{3} + \frac{2}{3} \cdot \frac{3}{2} = \frac{2}{3} \cdot \frac{3}{2}$

Step 2.1.1.11.2

Rewrite the expression.

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

Step 2.1.1.12

Cancel the common factor of $3$ .

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Step 2.1.1.12.1

Cancel the common factor.

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

Step 2.1.1.12.2

Rewrite the expression.

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

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $\frac{2}{3} \cdot \frac{3}{2}$ .

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Step 2.2.1.1

Cancel the common factor of $2$ .

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Step 2.2.1.1.1

Cancel the common factor.

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

Step 2.2.1.1.2

Rewrite the expression.

$\frac{7 n}{3} + 1 = \frac{1}{3} \cdot 3$

Step 2.2.1.2

Cancel the common factor of $3$ .

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Step 2.2.1.2.1

Cancel the common factor.

$\frac{7 n}{3} + 1 = \frac{1}{3} \cdot 3$

Step 2.2.1.2.2

Rewrite the expression.

$\frac{7 n}{3} + 1 = 1$

Step 3

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

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Step 3.1

Subtract $1$ from both sides of the equation.

$\frac{7 n}{3} = 1 - 1$

Step 3.2

Subtract $1$ from $1$ .

$\frac{7 n}{3} = 0$

Step 4

Set the numerator equal to zero.

$7 n = 0$

Step 5

Divide each term in $7 n = 0$ by $7$ and simplify.

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Step 5.1

Divide each term in $7 n = 0$ by $7$ .

$\frac{7 n}{7} = \frac{0}{7}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $7$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{7 n}{7} = \frac{0}{7}$

Step 5.2.1.2

Divide $n$ by $1$ .

$n = \frac{0}{7}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $0$ by $7$ .

$n = 0$