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

Summary

This 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.