Algebra Examples

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

Step 1

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

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Step 1.1

Rewrite.

$0 + 0 + \frac{1}{2} \cdot (- \frac{3}{2} n + 1) = \frac{3}{4} - n$

Step 1.2

Simplify by adding zeros.

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

Step 1.3

Simplify each term.

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Step 1.3.1

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

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

Step 1.3.2

Move $3$ to the left of $n$ .

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

Step 1.4

Apply the distributive property.

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

Step 1.5

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

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Step 1.5.1

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

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

Step 1.5.2

Multiply $2$ by $2$ .

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

Step 1.6

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

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

Step 2

Move all terms containing $n$ to the left side of the equation.

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Step 2.1

Add $n$ to both sides of the equation.

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

Step 2.2

To write $n$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

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

Step 2.3

Combine $n$ and $\frac{4}{4}$ .

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

Step 2.4

Combine the numerators over the common denominator.

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

Step 2.5

Add $- 3 n$ and $n \cdot 4$ .

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Step 2.5.1

Reorder $n$ and $4$ .

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

Step 2.5.2

Add $- 3 n$ and $4 \cdot n$ .

$\frac{n}{4} + \frac{1}{2} = \frac{3}{4}$

Step 3

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

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Step 3.1

Subtract $\frac{1}{2}$ from both sides of the equation.

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

Step 3.2

To write $- \frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 3.3

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.3.1

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

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

Step 3.3.2

Multiply $2$ by $2$ .

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

Step 3.4

Combine the numerators over the common denominator.

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

Step 3.5

Subtract $2$ from $3$ .

$\frac{n}{4} = \frac{1}{4}$

Step 4

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

$n = 1$