Precalculus Examples

$- 4 - 6 n = - 2 (2 n + 2) - 2 n$

Step 1

Since $n$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$- 2 (2 n + 2) - 2 n = - 4 - 6 n$

Step 2

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

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$- 2 (2 n) - 2 \cdot 2 - 2 n = - 4 - 6 n$

Step 2.1.2

Multiply $2$ by $- 2$ .

$- 4 n - 2 \cdot 2 - 2 n = - 4 - 6 n$

Step 2.1.3

Multiply $- 2$ by $2$ .

$- 4 n - 4 - 2 n = - 4 - 6 n$

Step 2.2

Subtract $2 n$ from $- 4 n$ .

$- 6 n - 4 = - 4 - 6 n$

Step 3

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

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Step 3.1

Add $6 n$ to both sides of the equation.

$- 6 n - 4 + 6 n = - 4$

Step 3.2

Combine the opposite terms in $- 6 n - 4 + 6 n$ .

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Step 3.2.1

Add $- 6 n$ and $6 n$ .

$0 - 4 = - 4$

Step 3.2.2

Subtract $4$ from $0$ .

$- 4 = - 4$

Step 4

Since $- 4 = - 4$ , the equation will always be true for any value of $n$ .

All real numbers

Step 5

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$