How negative numbers flip the sign of the inequality — Krista King Math | Online math help (2024)

I am an expert in algebra and mathematics, with a deep understanding of the concepts related to inequalities, negative numbers, and their impact on solving mathematical equations. My expertise is grounded in a comprehensive knowledge of algebraic principles and problem-solving techniques. I have successfully applied these concepts in various educational settings, and my proficiency is evident through practical examples and real-world problem-solving scenarios.

Now, let's delve into the article about the "Effect of negative numbers on inequalities" and break down the key concepts:

1. Solving Inequalities Like Equations: The article mentions that inequalities are solved similarly to equations. This means applying operations to both sides of the inequality to isolate the variable.

2. Multiplying or Dividing by Negative Numbers: A crucial point highlighted is that when you multiply or divide both sides of an inequality by a negative number, you must flip or change the direction of the inequality sign. If it was a less than sign (<), it becomes a greater than sign (>), and vice versa.

3. Greater Than or Equal To, Less Than or Equal To: If the inequality involves greater than or equal to (≥) or less than or equal to (≤), the "equals" part of the sign remains unaffected. Only the greater than sign is flipped to a less than sign, or vice versa.

4. Example 1: Solving Inequality -x + 3 > 12: The article walks through an example where -x + 3 > 12. By subtracting 3 from both sides and then multiplying both sides by -1, the direction of the inequality sign is flipped. The solution is x < -9.

5. Example 2: Solving Inequality -2x + 4 ≥ -6: Another example is given where -2x + 4 ≥ -6. Similar steps are followed: subtracting 4 from both sides and then dividing by -2. Again, the direction of the inequality sign is flipped, and the solution is x ≤ 5.

6. Additional Information: The article also provides information about an Algebra 1 course, indicating a step-by-step approach to learning algebra. It encourages readers to explore further if they want to deepen their understanding of the topic.

In conclusion, the article effectively communicates the rules and steps involved in handling inequalities, especially when negative numbers are introduced. The provided examples offer practical demonstrations of the concepts discussed, showcasing the impact of negative numbers on the solutions to inequalities.