Which Shows How To Solve The Equation $\frac{3}{4} X = -6$ For $x$ In One Step?A. $\frac{4}{3}\left(\frac{3}{4}\right) X = -6\left(\frac{4}{3}\right$\]B. $4\left(\frac{3}{4}\right) X = -6(4$\]C.

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Introduction

Solving equations is a fundamental concept in mathematics, and it's essential to understand how to solve them efficiently. In this article, we will focus on solving the equation 34x=−6\frac{3}{4} x = -6 for xx in one step. We will explore the different methods and techniques used to solve this equation and provide a step-by-step guide on how to do it.

Understanding the Equation

The equation 34x=−6\frac{3}{4} x = -6 is a linear equation, where xx is the variable we need to solve for. The equation is in the form of a fraction, where the numerator is 33 and the denominator is 44. The equation states that the product of 34\frac{3}{4} and xx is equal to −6-6.

Method A: Using Multiplication

One way to solve the equation 34x=−6\frac{3}{4} x = -6 is by using multiplication. To do this, we need to multiply both sides of the equation by the reciprocal of 34\frac{3}{4}, which is 43\frac{4}{3}.

Step 1: Multiply both sides by the reciprocal

43(34)x=−6(43)\frac{4}{3}\left(\frac{3}{4}\right) x = -6\left(\frac{4}{3}\right)

Step 2: Simplify the equation

4x=−84x = -8

Step 3: Solve for x

x=−2x = -2

Method B: Using Division

Another way to solve the equation 34x=−6\frac{3}{4} x = -6 is by using division. To do this, we need to divide both sides of the equation by 34\frac{3}{4}.

Step 1: Divide both sides by the fraction

134x=−634\frac{1}{\frac{3}{4}} x = \frac{-6}{\frac{3}{4}}

Step 2: Simplify the equation

43x=−8\frac{4}{3} x = -8

Step 3: Solve for x

x=−2x = -2

Method C: Using Inverse Operations

A third way to solve the equation 34x=−6\frac{3}{4} x = -6 is by using inverse operations. To do this, we need to multiply both sides of the equation by the reciprocal of 34\frac{3}{4}, which is 43\frac{4}{3}.

Step 1: Multiply both sides by the reciprocal

43(34)x=−6(43)\frac{4}{3}\left(\frac{3}{4}\right) x = -6\left(\frac{4}{3}\right)

Step 2: Simplify the equation

4x=−84x = -8

Step 3: Solve for x

x=−2x = -2

Conclusion

In conclusion, there are several methods to solve the equation 34x=−6\frac{3}{4} x = -6 for xx in one step. We have explored three different methods: using multiplication, using division, and using inverse operations. Each method provides a step-by-step guide on how to solve the equation efficiently. By understanding these methods, you will be able to solve linear equations with ease.

Tips and Tricks

  • When solving linear equations, it's essential to understand the concept of inverse operations.
  • Using multiplication or division can help simplify the equation and make it easier to solve.
  • Make sure to simplify the equation before solving for the variable.
  • Practice solving linear equations to become more comfortable with the different methods and techniques.

Common Mistakes

  • Not simplifying the equation before solving for the variable.
  • Not using the correct method to solve the equation.
  • Not checking the solution to ensure it's correct.

Real-World Applications

Solving linear equations is a fundamental concept in mathematics, and it has numerous real-world applications. Some examples include:

  • Calculating the cost of goods and services.
  • Determining the amount of time it takes to complete a task.
  • Solving problems in physics, engineering, and economics.

Introduction

Solving equations is a fundamental concept in mathematics, and it's essential to understand how to solve them efficiently. In this article, we will provide a Q&A guide on how to solve the equation 34x=−6\frac{3}{4} x = -6 for xx in one step. We will cover common questions and answers related to solving linear equations.

Q: What is the first step in solving a linear equation?

A: The first step in solving a linear equation is to simplify the equation by combining like terms and eliminating any fractions.

Q: How do I simplify a linear equation?

A: To simplify a linear equation, you can multiply both sides of the equation by the reciprocal of the fraction. For example, if the equation is 34x=−6\frac{3}{4} x = -6, you can multiply both sides by 43\frac{4}{3} to get rid of the fraction.

Q: What is the difference between multiplying and dividing in solving linear equations?

A: Multiplying and dividing are two different methods used to solve linear equations. Multiplying involves multiplying both sides of the equation by a number, while dividing involves dividing both sides of the equation by a number.

Q: How do I know which method to use when solving a linear equation?

A: The method you use to solve a linear equation depends on the equation itself. If the equation has a fraction, you may need to multiply both sides by the reciprocal of the fraction. If the equation has a decimal, you may need to multiply both sides by a power of 10.

Q: What is the inverse operation of multiplication?

A: The inverse operation of multiplication is division. When you multiply two numbers together, you can undo the multiplication by dividing the result by one of the numbers.

Q: How do I check my solution to a linear equation?

A: To check your solution to a linear equation, you can plug the solution back into the original equation and see if it's true. If the solution satisfies the equation, then it's correct.

Q: What are some common mistakes to avoid when solving linear equations?

A: Some common mistakes to avoid when solving linear equations include:

  • Not simplifying the equation before solving for the variable.
  • Not using the correct method to solve the equation.
  • Not checking the solution to ensure it's correct.

Q: How do I apply linear equations to real-world problems?

A: Linear equations can be applied to a wide range of real-world problems, including:

  • Calculating the cost of goods and services.
  • Determining the amount of time it takes to complete a task.
  • Solving problems in physics, engineering, and economics.

Conclusion

In conclusion, solving linear equations is a fundamental concept in mathematics, and it's essential to understand how to solve them efficiently. By following the steps outlined in this Q&A guide, you will be able to solve linear equations with ease and apply mathematical concepts to real-world problems.

Tips and Tricks

  • Practice solving linear equations to become more comfortable with the different methods and techniques.
  • Use a calculator to check your solutions and ensure they're correct.
  • Break down complex problems into smaller, more manageable parts.

Common Questions

  • Q: What is the difference between a linear equation and a quadratic equation? A: A linear equation is an equation in which the highest power of the variable is 1, while a quadratic equation is an equation in which the highest power of the variable is 2.
  • Q: How do I solve a linear equation with a variable on both sides? A: To solve a linear equation with a variable on both sides, you can add or subtract the same value to both sides of the equation to isolate the variable.
  • Q: What is the inverse operation of addition? A: The inverse operation of addition is subtraction. When you add two numbers together, you can undo the addition by subtracting one of the numbers from the result.