# Solve And Graph An Inequality - Reversing The SIgn

#### This video shows how to solve and graph an inequality. This example requires that you reverse the sign when solving.

Solve and graph the inequality $$3 < -5n + 2n$$, following these steps:

1. Combine Like Terms: Combine the like terms on the right side of the inequality.
$3 < -5n + 2n$
$3 < -3n$

2. Divide Both Sides by -3: To isolate $$n$$, divide both sides of the inequality by -3. Remember, when dividing or multiplying by a negative number, you must flip the inequality sign.
$\frac{3}{-3} > \frac{-3n}{-3}$
$-1 > n$

3. Write the Solution: The solution is $$n$$ is less than -1, written as $$n < -1$$.

4. Graph the Solution on a Number Line:
- Draw a number line.
- Mark the point -1 with an open circle, indicating that -1 is not included in the solution (since the inequality is strict, not "less than or equal to").
- Shade the region to the left of -1 to represent all values of $$n$$ that satisfy the inequality.

5. Label the Graph: Label the graph with an arrow pointing to the left and label it as $$n < -1$$.

The graph should show that all values of $$n$$ less than -1 satisfy the inequality.

In summary, the solution to the inequality $$3 < -5n + 2n$$ is $$n < -1$$, and the graph on the number line represents this solution as all values of $$n$$ less than -1.