Rational equations intro | Algebra 2 | Khan Academy | Summary and Q&A

TL;DR

Learn how to solve an equation for x by getting rid of denominators and isolating x.

Key Insights

• ☺️ Solving an equation for x often requires algebraic manipulations to get rid of denominators and isolate x.
• 🙃 Multiplying both sides of the equation by a suitable value can eliminate denominators.
• 😑 It is essential to check if the solution is consistent with the original expression to avoid undefined values.
• ☺️ The solution to the equation x + (1/9) - x = 2/3 is x = 3, satisfying the equation and not resulting in a zero denominator.

Transcript

• [Instructor] Let's say we wanna solve the following equation for x. We have x plus one over nine minus x is equal to 2/3. Pause this video and see if you can try this before we work through it together. All right now let's work through this together. Now, the first thing that we might wanna do, there's several ways that you could approach this, b... Read More

Questions & Answers

Q: What is the first step in solving the equation x + (1/9) - x = 2/3?

The first step is to eliminate the denominator by multiplying both sides of the equation by (9 - x). However, it is crucial to remember that x cannot be equal to 9 to avoid division by zero.

Q: How does the equation simplify after performing algebraic manipulations?

After canceling out terms and rearranging, the equation simplifies to 5/3x + 1 = 6.

Q: What is the final step in isolating x?

The final step involves subtracting 1 from both sides to get 5/3x = 5. Then, multiplying both sides by the reciprocal of 5/3 (which is 3/5) isolates x.

Q: Why is it important to check if the solution is consistent with the original expression?

Checking for consistency ensures that the solution doesn't result in a zero denominator. If x = 9, the original expression would be undefined.

Summary & Key Takeaways

• The video demonstrates how to solve the equation x + (1/9) - x = 2/3.

• The first step is to eliminate the denominator by multiplying both sides of the equation by (9 - x).

• It is important to note that x cannot be equal to 9 to avoid division by zero.

• By performing algebraic manipulations, the equation simplifies to 5/3x + 1 = 6.

• Isolating x involves subtracting 1 from both sides and then multiplying by the reciprocal of 5/3.

• The solution is x = 3, which is consistent with the original expression.