Linear Algebra Examples

$0.5 (2 n - 3) - 0.1 = 0.4 (6 + 2 n)$

Step 1

Simplify $0.5 (2 n - 3) - 0.1$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$0.5 (2 n) + 0.5 \cdot - 3 - 0.1 = 0.4 (6 + 2 n)$

Step 1.1.2

Multiply $0.5 (2 n)$ .

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Step 1.1.2.1

Multiply $2$ by $0.5$ .

$1 n + 0.5 \cdot - 3 - 0.1 = 0.4 (6 + 2 n)$

Step 1.1.2.2

Multiply $n$ by $1$ .

$n + 0.5 \cdot - 3 - 0.1 = 0.4 (6 + 2 n)$

Step 1.1.3

Multiply $0.5$ by $- 3$ .

$n - 1.5 - 0.1 = 0.4 (6 + 2 n)$

Step 1.2

Subtract $0.1$ from $- 1.5$ .

$n - 1.6 = 0.4 (6 + 2 n)$

Step 2

Simplify $0.4 (6 + 2 n)$ .

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Step 2.1

Apply the distributive property.

$n - 1.6 = 0.4 \cdot 6 + 0.4 (2 n)$

Step 2.2

Multiply.

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Step 2.2.1

Multiply $0.4$ by $6$ .

$n - 1.6 = 2.4 + 0.4 (2 n)$

Step 2.2.2

Multiply $2$ by $0.4$ .

$n - 1.6 = 2.4 + 0.8 n$

Step 3

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

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Step 3.1

Subtract $0.8 n$ from both sides of the equation.

$n - 1.6 - 0.8 n = 2.4$

Step 3.2

Subtract $0.8 n$ from $n$ .

$0.2 n - 1.6 = 2.4$

Step 4

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

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Step 4.1

Add $1.6$ to both sides of the equation.

$0.2 n = 2.4 + 1.6$

Step 4.2

Add $2.4$ and $1.6$ .

$0.2 n = 4$

Step 5

Divide each term in $0.2 n = 4$ by $0.2$ and simplify.

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Step 5.1

Divide each term in $0.2 n = 4$ by $0.2$ .

$\frac{0.2 n}{0.2} = \frac{4}{0.2}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $0.2$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{0.2 n}{0.2} = \frac{4}{0.2}$

Step 5.2.1.2

Divide $n$ by $1$ .

$n = \frac{4}{0.2}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $4$ by $0.2$ .

$n = 20$

Step 6

The domain is the set of all valid $n$ values.

${n | n = 20}$

Step 7