Add constants to both sides

Oct 13, 2025 by miodeya.com 11 views

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Introduction

Linear equations are a fundamental concept in mathematics, and solving them is a crucial skill for students to master. In this article, we will focus on solving a specific linear equation, and we will guide you through the step-by-step process to find the solution.

The Equation

The given equation is:

$-4 + 5x - 7 = 10 + 3x - 2x$

Our goal is to isolate the variable $x$ and find its value.

Step 1: Simplify the Equation

The first step in solving the equation is to simplify it by combining like terms. We can start by combining the constants on the left-hand side of the equation:

$-4 - 7 + 5x = 10 + 3x - 2x$

This simplifies to:

$-11 + 5x = 10 + x$

Step 2: Isolate the Variable

Next, we need to isolate the variable $x$ by getting all the terms with $x$ on one side of the equation. We can do this by subtracting $x$ from both sides of the equation:

$-11 + 5x - x = 10$

This simplifies to:

$-11 + 4x = 10$

Step 3: Add Constants to Both Sides

Now, we need to get rid of the constant term on the left-hand side of the equation. We can do this by adding $11$ to both sides of the equation:

$-11 + 11 + 4x = 10 + 11$

This simplifies to:

$4x = 21$

Step 4: Solve for $x$

Finally, we can solve for $x$ by dividing both sides of the equation by $4$ :

$x = \frac{21}{4}$

Conclusion

In this article, we solved a linear equation step by step. We simplified the equation, isolated the variable, added constants to both sides, and finally solved for $x$ . The solution to the equation is $x = \frac{21}{4}$ .

Discussion

Now that we have solved the equation, let's discuss the different options provided:

A. $x = \frac{21}{4}$ B. $x = \frac{4}{13}$ C. $x = \frac{13}{4}$ D. $x = \frac{4}{21}$

Based on our solution, we can see that option A is the correct answer.

Why is Option A Correct?

Option A is correct because it matches the solution we obtained by solving the equation. The other options do not match the solution, and therefore, they are incorrect.

What is the Importance of Solving Linear Equations?

Solving linear equations is an essential skill in mathematics, and it has numerous applications in real-life situations. Some of the importance of solving linear equations include:

Problem-solving: Solving linear equations helps us to solve problems in various fields, such as physics, engineering, and economics.
Critical thinking: Solving linear equations requires critical thinking and analytical skills, which are essential for making informed decisions.
Mathematical modeling: Solving linear equations helps us to create mathematical models that can be used to describe real-world phenomena.

Conclusion

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Introduction

In our previous article, we solved a linear equation step by step and found the solution. In this article, we will answer some frequently asked questions (FAQs) related to solving linear equations.

Q: What is a linear equation?

A: A linear equation is an equation in which the highest power of the variable(s) is 1. In other words, a linear equation is an equation that can be written in the form:

$a + bx = c$

where $a$ , $b$ , and $c$ are constants, and $x$ is the variable.

Q: What are the steps to solve a linear equation?

A: The steps to solve a linear equation are:

Simplify the equation: Combine like terms on both sides of the equation.
Isolate the variable: Get all the terms with the variable on one side of the equation.
Add constants to both sides: Get rid of any constant terms on the left-hand side of the equation.
Solve for the variable: Divide both sides of the equation by the coefficient of the variable.

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(s) is 1, whereas a quadratic equation is an equation in which the highest power of the variable(s) is 2. In other words, a linear equation is an equation that can be written in the form:

$a + bx = c$

where $a$ , $b$ , and $c$ are constants, and $x$ is the variable, whereas a quadratic equation is an equation that can be written in the form:

$a + bx + cx^2 = d$

where $a$ , $b$ , $c$ , and $d$ are constants, and $x$ is the variable.

Q: How do I know if an equation is linear or quadratic?

A: To determine if an equation is linear or quadratic, you need to look at the highest power of the variable(s) in the equation. If the highest power is 1, then the equation is linear. If the highest power is 2, then the equation is quadratic.

Q: Can I use the same steps to solve a quadratic equation?

A: No, you cannot use the same steps to solve a quadratic equation. Quadratic equations require a different set of steps to solve, which include factoring, using the quadratic formula, or completing the square.

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: Failing to combine like terms on both sides of the equation.
Not isolating the variable: Failing to get all the terms with the variable on one side of the equation.
Not adding constants to both sides: Failing to get rid of any constant terms on the left-hand side of the equation.
Not solving for the variable: Failing to divide both sides of the equation by the coefficient of the variable.

Conclusion

In conclusion, solving linear equations is a crucial skill in mathematics, and it has numerous applications in real-life situations. By following the step-by-step process outlined in this article, we can solve linear equations and find the solution. We also answered some frequently asked questions related to solving linear equations, including the difference between linear and quadratic equations, and common mistakes to avoid when solving linear equations.

Additional Resources

If you want to learn more about solving linear equations, here are some additional resources:

Textbooks: There are many textbooks available that cover solving linear equations, including "Algebra" by Michael Artin and "Linear Algebra and Its Applications" by Gilbert Strang.
Online resources: There are many online resources available that cover solving linear equations, including Khan Academy, MIT OpenCourseWare, and Wolfram Alpha.
Practice problems: There are many practice problems available that can help you practice solving linear equations, including those found on websites such as Mathway and Symbolab.