Fill In 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 $x = \square$.

Feb 27, 2025 by ADMIN 231 views

**Solving Two-Step Equations: A Step-by-Step Guide**

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 provide a detailed explanation of each step.

Understanding the Equation

Before we begin solving the equation, let's understand what it represents. The equation $5.1 = -3x - 4.2$ is a linear equation in one variable, where $x$ is the unknown variable. The equation states that the value of $5.1$ is equal to the value of $-3x$ minus $4.2$ . Our goal is to isolate the variable $x$ and find its value.

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 get rid of the negative term on the right-hand side of the equation.

$5.1 = -3x - 4.2$
$5.1 + 4.2 = -3x - 4.2 + 4.2$
$9.3 = -3x$

By adding $4.2$ to both sides of the equation, we have simplified the equation and isolated the term with the variable $x$ .

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 $x$ and find its value.

$9.3 = -3x$
$\frac{9.3}{-3} = \frac{-3x}{-3}$
$-3.1 = x$

By dividing both sides of the equation by $-3$ , we have isolated the variable $x$ and found its value.

Conclusion

In this article, we have guided you through the process of solving a two-step equation using a step-by-step approach. We have used the equation $5.1 = -3x - 4.2$ as an example and provided a detailed explanation of each step. By following these steps, you can solve any two-step equation and find the value of the unknown variable.

Tips and Tricks

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

Always start by simplifying the equation and isolating the term with the variable.
Use inverse operations to get rid of the negative term on the right-hand side of the equation.
Divide both sides of the equation by the coefficient of the variable to isolate the variable.
Check your answer by plugging it back into the original equation.

Practice Problems

Here are some practice problems to help you practice solving two-step equations:

$2.5 = 4x + 1.2$
$-2.1 = 3x - 1.5$
$4.9 = 2x + 2.1$

Introduction

Understanding the Equation

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 get rid of the negative term on the right-hand side of the equation.

$5.1 = -3x - 4.2$
$5.1 + 4.2 = -3x - 4.2 + 4.2$
$9.3 = -3x$

By adding $4.2$ to both sides of the equation, we have simplified the equation and isolated the term with the variable $x$ .

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 $x$ and find its value.

$9.3 = -3x$
$\frac{9.3}{-3} = \frac{-3x}{-3}$
$-3.1 = x$

By dividing both sides of the equation by $-3$ , we have isolated the variable $x$ and found its value.

Conclusion

Tips and Tricks

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

Always start by simplifying the equation and isolating the term with the variable.
Use inverse operations to get rid of the negative term on the right-hand side of the equation.
Divide both sides of the equation by the coefficient of the variable to isolate the variable.
Check your answer by plugging it back into the original equation.

Practice Problems

Here are some practice problems to help you practice solving two-step equations:

$2.5 = 4x + 1.2$
$-2.1 = 3x - 1.5$
$4.9 = 2x + 2.1$

Introduction

Understanding the Equation

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 get rid of the negative term on the right-hand side of the equation.

$5.1 = -3x - 4.2$
$5.1 + 4.2 = -3x - 4.2 + 4.2$
$9.3 = -3x$

By adding $4.2$ to both sides of the equation, we have simplified the equation and isolated the term with the variable $x$ .

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 $x$ and find its value.

$9.3 = -3x$
$\frac{9.3}{-3} = \frac{-3x}{-3}$
$-3.1 = x$

By dividing both sides of the equation by $-3$ , we have isolated the variable $x$ and found its value.

Conclusion

Tips and Tricks

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

Always start by simplifying the equation and isolating the term with the variable.
Use inverse operations to get rid of the negative term on the right-hand side of the equation.
Divide both sides of the equation by the coefficient of the variable to isolate the variable.
Check your answer by plugging it back into the original equation.

Practice Problems

Here are some practice problems to help you practice solving two-step equations:

$2.5
Solving Two-Step Equations: A Step-by-Step Guide =====================================================

Q&A: Frequently Asked Questions

Q: What is a two-step equation?

A: A two-step equation is a linear equation in one variable that requires two steps to solve. It is a fundamental concept in algebra and is used to solve problems in various fields, including science, engineering, and economics.

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

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

Simplify the equation by combining like terms.
Use inverse operations to get rid of the negative term on the right-hand side of the equation.
Divide both sides of the equation by the coefficient of the variable to isolate the variable.
Check your answer by plugging it back into the original equation.

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

A: A one-step equation is a linear equation in one variable that requires only one step to solve. It is a simple equation that can be solved by adding, subtracting, multiplying, or dividing both sides of the equation by a constant. A two-step equation, on the other hand, requires two steps to solve and involves more complex operations, such as using inverse operations and dividing both sides of the equation by a coefficient.

Q: How do I know which operation to use to solve a two-step equation?

A: To determine which operation to use to solve a two-step equation, you need to look at the equation and identify the term with the variable. If the term with the variable is negative, you need to use an inverse operation to get rid of the negative term. If the term with the variable is positive, you can simply divide both sides of the equation by the coefficient of the variable.

Q: What is the coefficient of a variable?

A: The coefficient of a variable is a constant that is multiplied by the variable. In a two-step equation, the coefficient of the variable is the number that is multiplied by the variable. For example, in the equation $2x = 4$ , the coefficient of the variable $x$ is $2$ .

Q: How do I check my answer to a two-step equation?

A: To check your answer to a two-step equation, you need to plug it back into the original equation and verify that it is true. If the equation is true, then your answer is correct. If the equation is not true, then you need to recheck your work and try again.

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 simplifying the equation before solving it.
Not using inverse operations to get rid of the negative term on the right-hand side of the equation.
Not dividing both sides of the equation by the coefficient of the variable to isolate the variable.
Not checking your answer by plugging it back into the original equation.

Conclusion

In this article, we have provided a step-by-step guide to solving two-step equations. We have also answered some frequently asked questions about two-step equations and provided some tips and tricks to help you solve them. By following these steps and avoiding common mistakes, you can become proficient in solving two-step equations and apply them to real-world problems.

Practice Problems

Here are some practice problems to help you practice solving two-step equations:

$2.5 = 4x + 1.2$
$-2.1 = 3x - 1.5$
$4.9 = 2x + 2.1$

Introduction

Understanding the Equation

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 get rid of the negative term on the right-hand side of the equation.

$5.1 = -3x - 4.2$
$5.1 + 4.2 = -3x - 4.2 + 4.2$
$9.3 = -3x$

By adding $4.2$ to both sides of the equation, we have simplified the equation and isolated the term with the variable $x$ .

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 $x$ and find its value.

$9.3 = -3x$
$\frac{9.3}{-3} = \frac{-3x}{-3}$
$-3.1 = x$

By dividing both sides of the equation by $-3$ , we have isolated the variable $x$ and found its value.

Conclusion

Tips and Tricks

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

Always start by simplifying the equation and isolating the term with the variable.
Use inverse operations to get rid of the negative term on the right-hand side of the equation.
Divide both sides of the equation by the coefficient of the variable to isolate the variable.
Check your answer by plugging it back into the original equation.

Practice Problems

Here are some practice problems to help you practice solving two-step equations:

$2.5 = 4x + 1.2$
$-2.1 = 3x - 1.5$
$4.9 = 2x + 2.1$