Rational inequalities 2 | Polynomial and rational functions | Algebra II | Khan Academy

TL;DR

This video explains how to solve rational inequality problems using two different methods and provides step-by-step instructions.

Transcript

Let's tackle a slightly harder problem than what we saw in the last video. I have here x minus 3 over x plus 4 is greater than or equal to 2. So the reason why this is slightly harder is I now have a greater than or equal to. And the other thing that makes it slightly harder is I don't just have a simple 0 here, I actually have a 2 here. So I'm goi... Read More

Key Insights

• 🤘 Solving rational inequality problems requires careful consideration of the signs of both the numerator and the denominator.
• 🙃 Multiplying both sides of the equation by the denominator can simplify the problem but requires attention to the signs and constraints.
• 0️⃣ Excluding values that make the denominator zero is essential to avoid undefined solutions.
• ❎ If both the numerator and the denominator are negative, the problem is not solvable.

Questions & Answers

Q: What is the challenge in solving a rational inequality problem with a greater than or equal to symbol?

The challenge is that both the numerator and the denominator can have different signs and require careful consideration of the constraints of the equation.

Q: How can you solve a rational inequality by multiplying both sides by the denominator?

By multiplying both sides by the denominator, you need to carefully consider the sign of the denominator and whether it is greater than or less than zero. This determines whether the inequality sign remains the same or needs to be reversed.

Q: Why is it important to exclude values that make the denominator equal to zero?

Excluding values that make the denominator zero is crucial because it would make the equation undefined and not valid.

Q: What do you do when you have a rational inequality with both the numerator and the denominator negative?

A rational inequality with both the numerator and the denominator negative can never have a solution that satisfies both constraints and is therefore not solvable.

Summary & Key Takeaways

• The video demonstrates how to solve a rational inequality problem with a greater than or equal to symbol.

• Two different methods are used: multiplying both sides by the denominator and dividing both sides by the numerator.

• The video emphasizes the importance of carefully considering the signs of the expressions and the constraints of the equation.