Solve the Inequality for n 7-3n<=n+3

$7 - 3 n \leq n + 3$

Step 1

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

Subtract $n$ from both sides of the inequality.

$7 - 3 n - n \leq 3$

Subtract $n$ from $- 3 n$ .

$7 - 4 n \leq 3$

Step 2

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

Subtract $7$ from both sides of the inequality.

$- 4 n \leq 3 - 7$

Subtract $7$ from $3$ .

$- 4 n \leq - 4$

Step 3

Divide each term in $- 4 n \leq - 4$ by $- 4$ and simplify.

Divide each term in $- 4 n \leq - 4$ by $- 4$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 4 n}{- 4} \geq \frac{- 4}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 n}{- 4} \geq \frac{- 4}{- 4}$

Divide $n$ by $1$ .

$n \geq \frac{- 4}{- 4}$

Simplify the right side.

Divide $- 4$ by $- 4$ .

$n \geq 1$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$n \geq 1$

Interval Notation:

$[1, \infty)$

Solve the Inequality for n 7-3n<=n+3

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