Solve For X Using Cross Multiplication.${ \frac{x-3}{2} = \frac{x-4}{3} }$ { x = [?] \}

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Introduction

Cross multiplication is a technique used to solve linear equations in the form of fractions. It involves multiplying the numerator of one fraction by the denominator of the other fraction, and vice versa. This method is particularly useful when dealing with equations that have variables in the numerator and denominator. In this article, we will learn how to solve for x using cross multiplication.

Understanding the Concept

Before we dive into the solution, let's understand the concept of cross multiplication. When we have two fractions, say ab\frac{a}{b} and cd\frac{c}{d}, we can multiply the numerator of the first fraction by the denominator of the second fraction, and vice versa. This gives us the equation ad=bcad = bc. We can use this equation to solve for the variable x.

Step-by-Step Solution

Now, let's apply the concept of cross multiplication to the given equation:

x−32=x−43\frac{x-3}{2} = \frac{x-4}{3}

To solve for x, we will multiply the numerator of the first fraction by the denominator of the second fraction, and vice versa. This gives us:

(x−3)×3=(x−4)×2(x-3) \times 3 = (x-4) \times 2

Expanding the equation, we get:

3x−9=2x−83x - 9 = 2x - 8

Now, let's isolate the variable x by adding 9 to both sides of the equation:

3x=2x−8+93x = 2x - 8 + 9

Simplifying the equation, we get:

3x=2x+13x = 2x + 1

Subtracting 2x from both sides of the equation, we get:

x=1x = 1

Conclusion

In this article, we learned how to solve for x using cross multiplication. We applied the concept of cross multiplication to the given equation and solved for the variable x. The final answer is x = 1.

Example Problems

Here are a few example problems that you can try to practice your skills:

  1. x+24=x−13\frac{x+2}{4} = \frac{x-1}{3}
  2. x−12=x+35\frac{x-1}{2} = \frac{x+3}{5}
  3. x+43=x−24\frac{x+4}{3} = \frac{x-2}{4}

Tips and Tricks

Here are a few tips and tricks that you can use to solve for x using cross multiplication:

  • Make sure to multiply the numerator of the first fraction by the denominator of the second fraction, and vice versa.
  • Simplify the equation by combining like terms.
  • Isolate the variable x by adding or subtracting the same value from both sides of the equation.
  • Check your answer by plugging it back into the original equation.

Common Mistakes

Here are a few common mistakes that you can avoid when solving for x using cross multiplication:

  • Not multiplying the numerator of the first fraction by the denominator of the second fraction, and vice versa.
  • Not simplifying the equation by combining like terms.
  • Not isolating the variable x by adding or subtracting the same value from both sides of the equation.
  • Not checking your answer by plugging it back into the original equation.

Real-World Applications

Cross multiplication has many real-world applications in fields such as physics, engineering, and economics. For example, it can be used to solve problems involving motion, forces, and energies. It can also be used to model and analyze complex systems, such as financial markets and supply chains.

Conclusion

Introduction

In our previous article, we learned how to solve for x using cross multiplication. We applied the concept of cross multiplication to a linear equation and solved for the variable x. In this article, we will answer some frequently asked questions about solving for x using cross multiplication.

Q: What is cross multiplication?

A: Cross multiplication is a technique used to solve linear equations in the form of fractions. It involves multiplying the numerator of one fraction by the denominator of the other fraction, and vice versa.

Q: When can I use cross multiplication?

A: You can use cross multiplication when you have a linear equation in the form of fractions, and you want to solve for the variable x.

Q: How do I apply cross multiplication to a linear equation?

A: To apply cross multiplication to a linear equation, you need to multiply the numerator of the first fraction by the denominator of the second fraction, and vice versa. This gives you the equation ad = bc.

Q: What if I have a fraction with a variable in the denominator? Can I still use cross multiplication?

A: Yes, you can still use cross multiplication even if you have a fraction with a variable in the denominator. However, you need to be careful when multiplying the numerator of the first fraction by the denominator of the second fraction, and vice versa.

Q: How do I simplify the equation after applying cross multiplication?

A: After applying cross multiplication, you need to simplify the equation by combining like terms. This will help you isolate the variable x.

Q: What if I get a negative value for x? Is that possible?

A: Yes, it is possible to get a negative value for x. However, you need to check your answer by plugging it back into the original equation to make sure it is correct.

Q: Can I use cross multiplication to solve quadratic equations?

A: No, you cannot use cross multiplication to solve quadratic equations. Cross multiplication is only used to solve linear equations in the form of fractions.

Q: What are some common mistakes to avoid when using cross multiplication?

A: Some common mistakes to avoid when using cross multiplication include:

  • Not multiplying the numerator of the first fraction by the denominator of the second fraction, and vice versa.
  • Not simplifying the equation by combining like terms.
  • Not isolating the variable x by adding or subtracting the same value from both sides of the equation.
  • Not checking your answer by plugging it back into the original equation.

Q: How can I practice using cross multiplication?

A: You can practice using cross multiplication by working on example problems. Try to solve linear equations in the form of fractions using cross multiplication, and check your answers by plugging them back into the original equation.

Q: What are some real-world applications of cross multiplication?

A: Cross multiplication has many real-world applications in fields such as physics, engineering, and economics. For example, it can be used to solve problems involving motion, forces, and energies. It can also be used to model and analyze complex systems, such as financial markets and supply chains.

Conclusion

In conclusion, cross multiplication is a powerful technique used to solve linear equations in the form of fractions. By understanding the concept of cross multiplication and following the step-by-step solution outlined in this article, you can master the art of solving for x using cross multiplication.