College Algebra - MathHelp.com - 1000+ Online Math Lessons

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19 Aug 200802:51

Summary

TLDRThis video from YourTeacherComm teaches solving equations involving fractions. It demonstrates simplifying an equation by multiplying by 4x, leading to x squared plus 2x equals 48. The solution involves factoring to find x values of -8 and 6, ensuring these do not invalidate the original equation.

Takeaways

📚 The video is from YourTeacher.com, which offers over 450 complete math lessons.
🎥 The lessons include example videos, interactive practice problems, self-tests, and more.
✏️ Think of the one in the problem as one over one.
🔢 The common denominator for 4, 1, and X is 4X.
✖️ Multiply both sides of the equation by 4X to eliminate the fractions.
➗ When multiplying 4X times (X - 2) over 4, the 4s cancel, resulting in X times (X - 2).
➕ Multiply 4X times 1 to get 4X, and multiply 4X times 12 over X to get 48.
📐 Distributing through the parentheses results in X squared - 2X + 4X equals 48.
🧮 Simplify the left side to X squared + 2X equals 48.
⚖️ To solve the equation, set it to 0 by subtracting 48 from both sides: X squared + 2X - 48 equals 0.
🔧 Factor the equation to get (X + 8) times (X - 6) equals 0.
✔️ The solutions are X = -8 and X = 6, and neither solution makes a denominator in the original equation equal to 0.

Q & A

What is the common denominator for the terms in the given equation?
-The common denominator for 4, 1, and X is 4X.
Why do we multiply both sides of the equation by 4X?
-We multiply both sides by 4X to eliminate the fractions in the equation.
What happens when we multiply 4X times X minus 2 over 4?
-The 4s cancel out, leaving us with X times (X minus 2).
What is the result of multiplying 4X by 1?
-Multiplying 4X by 1 gives us positive 4X.
How do we simplify 4X times 12 over X?
-The Xs cancel out, leaving us with 12 times 4, which is 48.
What is the result after distributing through the parentheses?
-The result is X squared minus 2X plus 4X, which simplifies to X squared plus 2X.
Why do we need to set the equation equal to 0?
-We set the equation equal to 0 because it contains an X squared term, which requires us to factor the equation.
How do we move the 48 to the left side of the equation?
-We subtract 48 from both sides to get X squared plus 2X minus 48 equals 0.
What are the factors of the equation X squared plus 2X minus 48 equals 0?
-The factors are (X plus 8) and (X minus 6).
What is the solution set for the equation?
-The solution set is X equals -8 and X equals 6.
Why do we check the solutions to ensure they do not make a denominator in the original equation equal to 0?
-We check to ensure that the solutions are valid and do not cause division by zero in the original equation.