Algebra Examples

\frac{3}{2} - \frac{1}{2} n = 2 n + 3

$\frac{3}{2} - \frac{1}{2} n = 2 n + 3$

Step 1

Combine

n

$n$ and

\frac{1}{2}

$\frac{1}{2}$ .

\frac{3}{2} - \frac{n}{2} = 2 n + 3

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

Step 2

Move all terms containing

n

$n$ to the left side of the equation.

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Step 2.1

Subtract

2 n

$2 n$ from both sides of the equation.

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

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

Step 2.2

To write

- 2 n

$- 2 n$ as a fraction with a common denominator, multiply by

\frac{2}{2}

$\frac{2}{2}$ .

\frac{3}{2} - \frac{n}{2} - 2 n \cdot \frac{2}{2} = 3

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

Step 2.3

Combine

- 2 n

$- 2 n$ and

\frac{2}{2}

$\frac{2}{2}$ .

\frac{3}{2} - \frac{n}{2} + \frac{- 2 n \cdot 2}{2} = 3

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

Step 2.4

Combine the numerators over the common denominator.

\frac{3}{2} + \frac{- n - 2 n \cdot 2}{2} = 3

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

Step 2.5

Combine the numerators over the common denominator.

\frac{3 - n - 2 n \cdot 2}{2} = 3

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

Step 2.6

Multiply

2

$2$ by

- 2

$- 2$ .

\frac{3 - n - 4 n}{2} = 3

$\frac{3 - n - 4 n}{2} = 3$

Step 2.7

Subtract

4 n

$4 n$ from

- n

$- n$ .

\frac{3 - 5 n}{2} = 3

$\frac{3 - 5 n}{2} = 3$

\frac{3 - 5 n}{2} = 3

$\frac{3 - 5 n}{2} = 3$

Step 3

Multiply both sides by

2

$2$ .

\frac{3 - 5 n}{2} \cdot 2 = 3 \cdot 2

$\frac{3 - 5 n}{2} \cdot 2 = 3 \cdot 2$

Step 4

Simplify.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify

\frac{3 - 5 n}{2} \cdot 2

$\frac{3 - 5 n}{2} \cdot 2$ .

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Step 4.1.1.1

Cancel the common factor of

2

$2$ .

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Step 4.1.1.1.1

Cancel the common factor.

\frac{3 - 5 n}{2} \cdot 2 = 3 \cdot 2

$\frac{3 - 5 n}{2} \cdot 2 = 3 \cdot 2$

Step 4.1.1.1.2

Rewrite the expression.

3 - 5 n = 3 \cdot 2

$3 - 5 n = 3 \cdot 2$

3 - 5 n = 3 \cdot 2

$3 - 5 n = 3 \cdot 2$

Step 4.1.1.2

Reorder

3

$3$ and

- 5 n

$- 5 n$ .

- 5 n + 3 = 3 \cdot 2

$- 5 n + 3 = 3 \cdot 2$

- 5 n + 3 = 3 \cdot 2

$- 5 n + 3 = 3 \cdot 2$

- 5 n + 3 = 3 \cdot 2

$- 5 n + 3 = 3 \cdot 2$

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply

3

$3$ by

2

$2$ .

- 5 n + 3 = 6

$- 5 n + 3 = 6$

- 5 n + 3 = 6

$- 5 n + 3 = 6$

- 5 n + 3 = 6

$- 5 n + 3 = 6$

Step 5

Solve for

n

$n$ .

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Step 5.1

Move all terms not containing

n

$n$ to the right side of the equation.

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Step 5.1.1

Subtract

3

$3$ from both sides of the equation.

- 5 n = 6 - 3

$- 5 n = 6 - 3$

Step 5.1.2

Subtract

3

$3$ from

6

$6$ .

- 5 n = 3

$- 5 n = 3$

- 5 n = 3

$- 5 n = 3$

Step 5.2

Divide each term in

- 5 n = 3

$- 5 n = 3$ by

- 5

$- 5$ and simplify.

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Step 5.2.1

Divide each term in

- 5 n = 3

$- 5 n = 3$ by

- 5

$- 5$ .

\frac{- 5 n}{- 5} = \frac{3}{- 5}

$\frac{- 5 n}{- 5} = \frac{3}{- 5}$

Step 5.2.2

Simplify the left side.

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Step 5.2.2.1

Cancel the common factor of

- 5

$- 5$ .

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Step 5.2.2.1.1

Cancel the common factor.

\frac{- 5 n}{- 5} = \frac{3}{- 5}

$\frac{- 5 n}{- 5} = \frac{3}{- 5}$

Step 5.2.2.1.2

Divide

n

$n$ by

1

$1$ .

n = \frac{3}{- 5}

$n = \frac{3}{- 5}$

n = \frac{3}{- 5}

$n = \frac{3}{- 5}$

n = \frac{3}{- 5}

$n = \frac{3}{- 5}$

Step 5.2.3

Simplify the right side.

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Step 5.2.3.1

Move the negative in front of the fraction.

n = - \frac{3}{5}

$n = - \frac{3}{5}$

n = - \frac{3}{5}

$n = - \frac{3}{5}$

n = - \frac{3}{5}

$n = - \frac{3}{5}$

n = - \frac{3}{5}

$n = - \frac{3}{5}$

Step 6

The result can be shown in multiple forms.

Exact Form:

n = - \frac{3}{5}

$n = - \frac{3}{5}$

Decimal Form:

n = - 0.6

$n = - 0.6$