College Algebra - MathHelp.com - 1000+ Online Math Lessons
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
📚 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
💡fractions
💡distributing
💡x squared
💡quadratic equation
💡factoring
💡solution set
💡denominator
💡subtracting
💡interactive practice
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.
Transcripts
the following is a selected video from
your teacher comm where you can browse
over 450 complete math lessons with
example videos interactive practice
problems self tests and more try a
complete lesson today at your teacher
comm think of the one in this problem as
one over one the common denominator for
4 1 and X is 4x so 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 parentheses X minus 2 4x times
positive 1 is positive 4x and 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 and 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 so our next step
is to 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 so
either X plus 8 equals 0 or X minus 6
equals 0 which means that our solution
set is negative 8 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
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