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.

Outlines

00:00

📚 Math Lesson Overview

This paragraph introduces a comprehensive math learning platform, 'your teacher comm', which offers over 450 complete math lessons, including example videos, interactive practice, problems, self-tests, and more. It encourages the user to try a complete lesson to experience the platform's offerings.

🔍 Solving Equations with Fractions

The paragraph demonstrates a step-by-step solution to a math problem involving fractions. It explains the process of eliminating fractions by multiplying both sides of the equation by the common denominator, in this case, 4x. The equation is simplified to x squared plus 2x equals 48, and the solution involves factoring to find the roots of the equation, which are x = -8 and x = 6. The paragraph also emphasizes the importance of ensuring that the solutions do not invalidate the original equation by making any denominators equal to zero.

Mindmap

Keywords

💡common denominator

The common denominator is a shared multiple of the denominators of several fractions, allowing them to be combined or compared. In the video, the common denominator for the fractions in the equation is 4x, which is used to eliminate the fractions by multiplying both sides of the equation by 4x.

💡fractions

Fractions represent parts of a whole and are used in the video to illustrate how to solve equations involving fractional terms. By multiplying both sides of the equation by the common denominator, the fractions are eliminated, simplifying the equation.

💡distributing

Distributing refers to the process of multiplying each term inside a set of parentheses by a factor outside the parentheses. In the video, distributing 4x across the terms inside the parentheses results in x squared and 2x terms.

💡x squared

X squared, written as x^2, is a term that represents a variable raised to the power of two. It is a key component of quadratic equations. In the video, the equation simplifies to include an x squared term, indicating it is a quadratic equation.

💡quadratic equation

A quadratic equation is a second-degree polynomial equation in a single variable, typically in the form of ax^2 + bx + c = 0. The video discusses solving a quadratic equation by first setting it to zero and then factoring it.

💡factoring

Factoring involves breaking down an equation into simpler components, or factors, that when multiplied together give the original equation. In the video, the quadratic equation x^2 + 2x - 48 = 0 is factored into (x + 8)(x - 6) = 0.

💡solution set

The solution set is the set of all possible values that satisfy an equation. In the video, the solution set for the factored quadratic equation includes the values -8 and 6.

💡denominator

The denominator is the bottom part of a fraction that indicates the number of equal parts the whole is divided into. The video emphasizes checking that the solutions do not make the denominator zero, which would make the fraction undefined.

💡subtracting

Subtracting is the mathematical operation of taking one quantity away from another. In the video, 48 is subtracted from both sides of the equation to move all terms to one side, setting the quadratic equation to zero.

💡interactive practice

Interactive practice refers to engaging and participatory exercises designed to reinforce learning. The video mentions YourTeacher.com, which offers interactive practice problems to help students apply the concepts taught in the lessons.

Highlights

Think of the one in this problem as one over one.

The common denominator for 4, 1, and X is 4x.

Multiply both sides of the equation by 4x to get rid of the fractions.

When multiplying 4x times X minus 2 over 4, the 4s cancel and we have x times (X minus 2).

4x times positive 1 is positive 4x.

When multiplying 4x times 12 over X, the x's cancel and we have 12 times 4 or 48.

Distributing through the parentheses we have x squared minus 2x plus 4x equals 48.

Simplifying further on the left side, we have x squared plus 2x equals 48.

Notice that our equation has an x squared term in it.

In this situation, remember we must first set the equation equal to 0, then factor.

Move the 48 to the left side of the equation by subtracting 48 from both sides to get x squared plus 2x minus 48 equals 0.

Now we can factor to get (X plus 8) times (X minus 6) equals 0.

Either X plus 8 equals 0 or X minus 6 equals 0.

Our solution set is negative 8 and 6.

Finally, make sure that neither of our solutions will make a denominator in the original equation equals 0, which they don't, so we can keep both answers.