Pre-Algebra Examples

$\frac{1}{2} \cdot (12 n - 4) = 14 - 10 n$

Step 1

Simplify $\frac{1}{2} \cdot (12 n - 4)$ .

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Step 1.1

Rewrite.

$0 + 0 + \frac{1}{2} \cdot (12 n - 4) = 14 - 10 n$

Step 1.2

Simplify by adding zeros.

$\frac{1}{2} \cdot (12 n - 4) = 14 - 10 n$

Step 1.3

Apply the distributive property.

$\frac{1}{2} (12 n) + \frac{1}{2} \cdot - 4 = 14 - 10 n$

Step 1.4

Cancel the common factor of $2$ .

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Step 1.4.1

Factor $2$ out of $12 n$ .

$\frac{1}{2} (2 (6 n)) + \frac{1}{2} \cdot - 4 = 14 - 10 n$

Step 1.4.2

Cancel the common factor.

$\frac{1}{2} (2 (6 n)) + \frac{1}{2} \cdot - 4 = 14 - 10 n$

Step 1.4.3

Rewrite the expression.

$6 n + \frac{1}{2} \cdot - 4 = 14 - 10 n$

Step 1.5

Cancel the common factor of $2$ .

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Step 1.5.1

Factor $2$ out of $- 4$ .

$6 n + \frac{1}{2} \cdot (2 (- 2)) = 14 - 10 n$

Step 1.5.2

Cancel the common factor.

$6 n + \frac{1}{2} \cdot (2 \cdot - 2) = 14 - 10 n$

Step 1.5.3

Rewrite the expression.

$6 n - 2 = 14 - 10 n$

Step 2

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

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Step 2.1

Add $10 n$ to both sides of the equation.

$6 n - 2 + 10 n = 14$

Step 2.2

Add $6 n$ and $10 n$ .

$16 n - 2 = 14$

Step 3

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

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Step 3.1

Add $2$ to both sides of the equation.

$16 n = 14 + 2$

Step 3.2

Add $14$ and $2$ .

$16 n = 16$

Step 4

Divide each term in $16 n = 16$ by $16$ and simplify.

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Step 4.1

Divide each term in $16 n = 16$ by $16$ .

$\frac{16 n}{16} = \frac{16}{16}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $16$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{16 n}{16} = \frac{16}{16}$

Step 4.2.1.2

Divide $n$ by $1$ .

$n = \frac{16}{16}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $16$ by $16$ .

$n = 1$