Solve the Inequality for n 2(n-1)+4n=2(3n-1)

$2 (n - 1) + 4 n = 2 (3 n - 1)$

Simplify $2 (n - 1) + 4 n$ .

Simplify each term.

Apply the distributive property.

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

Multiply $2$ by $- 1$ .

$2 n - 2 + 4 n = 2 (3 n - 1)$

Add $2 n$ and $4 n$ .

$6 n - 2 = 2 (3 n - 1)$

Simplify $2 (3 n - 1)$ .

Apply the distributive property.

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

Multiply.

Multiply $3$ by $2$ .

$6 n - 2 = 6 n + 2 \cdot - 1$

Multiply $2$ by $- 1$ .

$6 n - 2 = 6 n - 2$

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

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

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

Combine the opposite terms in $6 n - 2 - 6 n$ .

Subtract $6 n$ from $6 n$ .

$0 - 2 = - 2$

Subtract $2$ from $0$ .

$- 2 = - 2$

Since $- 2 = - 2$ , the equation will always be true.

Always true

The result can be shown in multiple forms.

Always true

Interval Notation:

$(- \infty, \infty)$