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

MathHelp.com
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.

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Math LessonsInteractive PracticeSelf TestsEducational ContentOnline LearningExample VideosFractionsEquation SolvingAlgebraProblem Solving
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