Solve for n 2n-4<3n-6

$2 n - 4 < 3 n - 6$

Step 1

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

Subtract $3 n$ from both sides of the inequality.

$2 n - 4 - 3 n < - 6$

Subtract $3 n$ from $2 n$ .

$- n - 4 < - 6$

Step 2

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

Add $4$ to both sides of the inequality.

$- n < - 6 + 4$

Add $- 6$ and $4$ .

$- n < - 2$

Step 3

Divide each term in $- n < - 2$ by $- 1$ and simplify.

Divide each term in $- n < - 2$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- n}{- 1} > \frac{- 2}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{n}{1} > \frac{- 2}{- 1}$

Divide $n$ by $1$ .

$n > \frac{- 2}{- 1}$

Simplify the right side.

Divide $- 2$ by $- 1$ .

$n > 2$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$n > 2$

Interval Notation:

$(2, \infty)$

Solve for n 2n-4<3n-6

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