Finite Math Examples

$3 n - 2 + 2 (2 n + 1) = 5 n + 7 + n$

Step 1

Simplify $3 n - 2 + 2 (2 n + 1)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$3 n - 2 + 2 (2 n) + 2 \cdot 1 = 5 n + 7 + n$

Step 1.1.2

Multiply $2$ by $2$ .

$3 n - 2 + 4 n + 2 \cdot 1 = 5 n + 7 + n$

Step 1.1.3

Multiply $2$ by $1$ .

$3 n - 2 + 4 n + 2 = 5 n + 7 + n$

Step 1.2

Simplify by adding terms.

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Step 1.2.1

Combine the opposite terms in $3 n - 2 + 4 n + 2$ .

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Step 1.2.1.1

Add $- 2$ and $2$ .

$3 n + 4 n + 0 = 5 n + 7 + n$

Step 1.2.1.2

Add $3 n + 4 n$ and $0$ .

$3 n + 4 n = 5 n + 7 + n$

Step 1.2.2

Add $3 n$ and $4 n$ .

$7 n = 5 n + 7 + n$

Step 2

Add $5 n$ and $n$ .

$7 n = 6 n + 7$

Step 3

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

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Step 3.1

Subtract $6 n$ from both sides of the equation.

$7 n - 6 n = 7$

Step 3.2

Subtract $6 n$ from $7 n$ .

$n = 7$