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.

Related Articles