Fill The Empty Slots 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 = □ X = \square X = □

Introduction

Two-step equations are a fundamental concept in algebra, and solving them requires a clear understanding of the steps involved. In this article, we will guide you through the process of solving a two-step equation using a step-by-step approach. We will use the equation $5.1 = -3x - 4.2$ as an example and walk you through the solution.

Understanding Two-Step Equations

A two-step equation is an equation that requires two steps to solve. It is typically written in the form of $ax + b = cx + d$, where $a$, $b$, $c$, and $d$ are constants. The goal is to isolate the variable $x$ on one side of the equation.

Step 1: Add 4.2 to Both Sides

To solve the equation $5.1 = -3x - 4.2$, we need to add 4.2 to both sides of the equation. This will help us get rid of the negative term on the right-hand side.

# Define the equation
equation = "5.1 = -3x - 4.2"
new_equation = "5.1 + 4.2 = -3x + 4.2 + 4.2"

By adding 4.2 to both sides, we get:

$9.3 = -3x$

Step 2: Divide Both Sides by -3

Now that we have the equation $9.3 = -3x$, we need to divide both sides by -3 to isolate the variable $x$.

# Divide both sides by -3
new_equation = "9.3 / -3 = -3x / -3"

By dividing both sides by -3, we get:

$x = -3$

The Solution

Therefore, the solution to the two-step equation $5.1 = -3x - 4.2$ is $x = -3$.

Conclusion

Solving two-step equations requires a clear understanding of the steps involved. By following the steps outlined in this article, you can solve two-step equations with ease. Remember to add or subtract the same value to both sides of the equation and then divide or multiply both sides by the same value to isolate the variable.

Tips and Tricks

• Make sure to follow the order of operations (PEMDAS) when solving two-step equations.
• Use a calculator to check your solution.
• Practice solving two-step equations to become more comfortable with the process.

Common Mistakes

• Forgetting to add or subtract the same value to both sides of the equation.
• Forgetting to divide or multiply both sides by the same value.
• Not following the order of operations (PEMDAS).

Real-World Applications

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

• Finance: Calculating interest rates and investment returns.
• Science: Measuring the rate of change of a physical quantity.
• Engineering: Designing and optimizing systems.

Conclusion

Solving two-step equations is an essential skill in algebra and has many real-world applications. By following the steps outlined in this article, you can solve two-step equations with ease. Remember to practice solving two-step equations to become more comfortable with the process.

Additional Resources

• Khan Academy: Two-Step Equations
• Mathway: Two-Step Equations
• Wolfram Alpha: Two-Step Equations

Final Thoughts

Introduction

Solving two-step equations can be a challenging task, but with the right guidance, it can become a breeze. In this article, we will answer some of the most frequently asked questions about solving two-step equations.

Q: What is a two-step equation?

A two-step equation is an equation that requires two steps to solve. It is typically written in the form of $ax + b = cx + d$, where $a$, $b$, $c$, and $d$ are constants. The goal is to isolate the variable $x$ on one side of the equation.

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

To solve a two-step equation, you need to follow these steps:

1. Add or subtract the same value to both sides of the equation to get rid of the constant term on the right-hand side.
2. Divide or multiply both sides of the equation by the same value to isolate the variable $x$.

Q: What is the order of operations (PEMDAS)?

The order of operations (PEMDAS) is a set of rules that tells you which operations to perform first when solving an equation. The acronym PEMDAS stands for:

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 handle negative numbers in two-step equations?

When working with negative numbers in two-step equations, you need to be careful when adding or subtracting the same value to both sides of the equation. For example, if you have the equation $-3x = 4$, you need to add 3 to both sides of the equation to get rid of the negative term on the right-hand side.

Q: What is the difference between a two-step equation and a one-step equation?

A one-step equation is an equation that requires only one step to solve. It is typically written in the form of $ax = b$, where $a$ and $b$ are constants. A two-step equation, on the other hand, requires two steps to solve and is typically written in the form of $ax + b = cx + d$.

Q: Can I use a calculator to solve two-step equations?

Yes, you can use a calculator to solve two-step equations. However, it's always a good idea to check your solution by plugging it back into the original equation.

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

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

• Forgetting to add or subtract the same value to both sides of the equation.
• Forgetting to divide or multiply both sides of the equation by the same value.
• Not following the order of operations (PEMDAS).

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

You can practice solving two-step equations by working through a series of problems. You can find practice problems in your textbook or online. You can also try solving two-step equations on your own by creating your own problems.

Conclusion

Solving two-step equations can be a challenging task, but with the right guidance, it can become a breeze. By following the steps outlined in this article, you can solve two-step equations with ease. Remember to practice solving two-step equations to become more comfortable with the process.

Additional Resources

• Khan Academy: Two-Step Equations
• Mathway: Two-Step Equations
• Wolfram Alpha: Two-Step Equations

Final Thoughts

Solving two-step equations requires a clear understanding of the steps involved. By following the steps outlined in this article, you can solve two-step equations with ease. Remember to practice solving two-step equations to become more comfortable with the process.