Fill In The Empty Slot By Dragging Tiles From The Left To Show The Next Step For Solving The Equation.Solve The Two-step Equation: $\[ 5.1 = -3x - 4.2 \\]1. Add 4.2 To Both Sides.2. Divide Both Sides By -3.The Solution Is $\[ X = \square

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Introduction

Solving two-step equations is a fundamental concept in mathematics that requires a clear understanding of algebraic operations and their application to solve linear equations. In this article, we will delve into the world of two-step equations, exploring the steps involved in solving them and providing a step-by-step guide on how to tackle these equations.

What are Two-Step Equations?

Two-step equations are linear equations that require two steps to solve. These equations involve variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. The goal of solving a two-step equation is to isolate the variable, which represents the unknown value.

Example of a Two-Step Equation

Let's consider the following two-step equation:

5.1=−3x−4.2{ 5.1 = -3x - 4.2 }

To solve this equation, we need to follow the steps outlined below.

Step 1: Add 4.2 to Both Sides

The first step in solving the equation is to add 4.2 to both sides of the equation. This will help us isolate the term involving the variable.

5.1+4.2=−3x−4.2+4.2{ 5.1 + 4.2 = -3x - 4.2 + 4.2 }

Simplifying the equation, we get:

9.3=−3x{ 9.3 = -3x }

Step 2: Divide Both Sides by -3

The next step is to divide both sides of the equation by -3. This will help us isolate the variable.

9.3−3=−3x−3{ \frac{9.3}{-3} = \frac{-3x}{-3} }

Simplifying the equation, we get:

−3.1=x{ -3.1 = x }

The Solution

Therefore, the solution to the two-step equation is:

x=−3.1{ x = -3.1 }

Discussion

Solving two-step equations requires a clear understanding of algebraic operations and their application to solve linear equations. By following the steps outlined above, we can solve two-step equations and isolate the variable.

Tips and Tricks

Here are some tips and tricks to help you solve two-step equations:

  • Read the equation carefully: Before starting to solve the equation, read it carefully to understand the operations involved.
  • Follow the order of operations: When solving the equation, follow the order of operations (PEMDAS) to ensure that you perform the operations in the correct order.
  • Check your work: After solving the equation, check your work to ensure that you have isolated the variable correctly.

Conclusion

Solving two-step equations is a fundamental concept in mathematics that requires a clear understanding of algebraic operations and their application to solve linear equations. By following the steps outlined above and practicing regularly, you can become proficient in solving two-step equations and tackle more complex mathematical problems with confidence.

Practice Problems

Here are some practice problems to help you reinforce your understanding of two-step equations:

  1. Solve the equation: 2x+5=11{ 2x + 5 = 11 }
  2. Solve the equation: x−3=7{ x - 3 = 7 }
  3. Solve the equation: 4x−2=10{ 4x - 2 = 10 }

Answer Key

Here are the answers to the practice problems:

  1. x=3{ x = 3 }
  2. x=10{ x = 10 }
  3. x=3{ x = 3 }

References

  • Mathway: A online math problem solver that can help you solve two-step equations and other mathematical problems.
  • Khan Academy: A online learning platform that offers video lessons and practice exercises on two-step equations and other mathematical topics.
  • Math Open Reference: A online math reference book that offers detailed explanations and examples of two-step equations and other mathematical concepts.
    Frequently Asked Questions (FAQs) on Two-Step Equations ===========================================================

Q: What is a two-step equation?

A: A two-step equation is a linear equation that requires two steps to solve. These equations involve variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division.

Q: How do I solve a two-step equation?

A: To solve a two-step equation, follow these steps:

  1. Add or subtract the same value to both sides of the equation to isolate the term involving the variable.
  2. Multiply or divide both sides of the equation by the same value to isolate the variable.

Q: What is the order of operations in solving two-step equations?

A: The order of operations in solving two-step equations is:

  1. Parentheses: Evaluate expressions inside parentheses first.
  2. Exponents: Evaluate any exponential expressions next.
  3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
  4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: How do I check my work when solving a two-step equation?

A: To check your work when solving a two-step equation, follow these steps:

  1. Plug the solution back into the original equation to ensure that it is true.
  2. Simplify the equation to ensure that the solution is correct.

Q: What are some common mistakes to avoid when solving two-step equations?

A: Some common mistakes to avoid when solving two-step equations include:

  • Not following the order of operations: Failing to follow the order of operations can lead to incorrect solutions.
  • Not checking work: Failing to check work can lead to incorrect solutions.
  • Not simplifying the equation: Failing to simplify the equation can lead to incorrect solutions.

Q: How can I practice solving two-step equations?

A: There are many ways to practice solving two-step equations, including:

  • Using online resources: Websites such as Mathway and Khan Academy offer interactive practice exercises and video lessons on two-step equations.
  • Using worksheets: Worksheets can provide a structured way to practice solving two-step equations.
  • Working with a tutor: Working with a tutor can provide one-on-one instruction and feedback on solving two-step equations.

Q: What are some real-world applications of two-step equations?

A: Two-step equations have many real-world applications, including:

  • Science: Two-step equations are used to solve problems in physics, chemistry, and other scientific fields.
  • Engineering: Two-step equations are used to solve problems in engineering, including designing and building structures.
  • Finance: Two-step equations are used to solve problems in finance, including calculating interest rates and investment returns.

Q: How can I use technology to solve two-step equations?

A: There are many ways to use technology to solve two-step equations, including:

  • Using online calculators: Online calculators can provide a quick and easy way to solve two-step equations.
  • Using graphing calculators: Graphing calculators can provide a visual representation of the solution to a two-step equation.
  • Using computer algebra systems: Computer algebra systems can provide a step-by-step solution to a two-step equation.

Conclusion

Two-step equations are a fundamental concept in mathematics that require a clear understanding of algebraic operations and their application to solve linear equations. By following the steps outlined above and practicing regularly, you can become proficient in solving two-step equations and tackle more complex mathematical problems with confidence.