Number Line Graph
The number line graph below represents the compound inequality 2 < x < 5:
| —|—|—|—|—|—|—|—|—|—|—|—|—|—|—|—|—|—|—|—|—|—|—|—|—|—|—|—|—|—|—|—|—|—|—|—|—|—|—| |
| -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 |
The shaded region between 2 and 5 represents the solutions to the compound inequality. This indicates that x must be greater than 2 and less than 5 for the compound inequality to be true.
“Or” Compound Inequality
On the other hand, an “or” compound inequality is represented by the union of two separate inequalities. This means that the solution to the compound inequality is the combination of the solutions to the individual inequalities. Let’s consider the compound inequality x < -3 or x > 3. This can be represented on a number line graph as follows:
| —|—|—|—|—|—|—|—|—|—|—|—|—|—|—|—|—|—|—|—|—|—|—|—|—|—|—|—|—|—|—|—|—|—|—|—|—|—|—|—|—| |
| -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 |
The shaded regions to the left of -3 and to the right of 3 represent the solutions to the compound inequality. This indicates that x must be less than -3 or greater than 3 for the compound inequality to be true.
Conclusion
Understanding how compound inequalities can be represented by graphs is a fundamental aspect of algebraic reasoning. By visualizing the solutions to compound inequalities, we can gain valuable insights into their behavior and relationships. Whether it’s an “and” compound inequality or an “or” compound inequality, being able to interpret and graphically represent these concepts is a key skill for anyone studying mathematics. We hope this article has provided you with a clearer understanding of how compound inequalities can be represented by graphs.
Remember, practice makes perfect, so don’t hesitate to try creating and graphing your own compound inequalities to solidify your understanding of this important mathematical concept.
Thank you for reading!
