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Questions and Answers
Which of the following is a possible solution for the equation $\frac{x}{2} + \frac{y}{x+10} = \frac{3}{4}$?
Which of the following is a possible solution for the equation $\frac{x}{2} + \frac{y}{x+10} = \frac{3}{4}$?
Which of the following is NOT a possible solution for the equation $\frac{x}{2} + \frac{y}{x+10} = \frac{3}{4}$?
Which of the following is NOT a possible solution for the equation $\frac{x}{2} + \frac{y}{x+10} = \frac{3}{4}$?
What is the value of $y$ when $x = -5$ in the equation $\frac{x}{2} + \frac{y}{x+10} = \frac{3}{4}$?
What is the value of $y$ when $x = -5$ in the equation $\frac{x}{2} + \frac{y}{x+10} = \frac{3}{4}$?
Какие числа являются расширениями рациональных чисел?
Какие числа являются расширениями рациональных чисел?
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Что такое мнимые числа?
Что такое мнимые числа?
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Что является расширением целых чисел?
Что является расширением целых чисел?
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Какие числа являются расширениями натуральных чисел?
Какие числа являются расширениями натуральных чисел?
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Study Notes
Equation Solutions
- The equation to solve is (\frac{x}{2} + \frac{y}{x+10} = \frac{3}{4}).
- Possible solutions can include various pairs of ((x, y)) that satisfy the equation.
- To check if a specific pair is a solution, substitute the values into the equation and verify if the left-hand side equals (\frac{3}{4}).
- Identifying a value that does not meet this condition indicates it is not a solution.
Finding (y) for Specific (x)
- Substitute (x = -5) into the equation (\frac{-5}{2} + \frac{y}{-5+10} = \frac{3}{4}).
- Calculate how (\frac{-5}{2}) is evaluated and then solve for (y) as follows:
- (\frac{-5}{10} + \frac{y}{5} = \frac{3}{4})
- Rearranging leads to finding (y).
Extensions of Number Sets
- Rational number extensions include all numbers that can be expressed as a fraction of integers, as well as certain additional numbers such as square roots or other algebraic numbers.
- Imaginary numbers are defined as (a + bi) where (i) is the square root of (-1), providing solutions to equations that lack real solutions.
- Integer extensions include rational numbers, where every integer can be expressed in fraction form.
- Natural number extensions may involve whole numbers, integers, and fractions, broadening the concept of counting.
Summary of Number Extensions
- Rational numbers extend to include irrational numbers.
- Imaginary numbers comprise a separate category outside the reals, essential in complex number theory.
- Whole numbers include all integers (positive, negative, and zero).
- Natural numbers can potentially expand into greater realms like integers and rational numbers.
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Description
Test your knowledge of solving equations with fractions in this quiz. Determine possible solutions, identify non-solutions, and find the value of a variable given a specific value.
