Mariena Solved The Equation 2 X + 5 = − 10 − X 2x + 5 = -10 - X 2 X + 5 = − 10 − X . Her Steps Are Shown Below:1. 2 X + 5 = − 10 − X 2x + 5 = -10 - X 2 X + 5 = − 10 − X Step 1: 3 X + 5 = − 10 3x + 5 = -10 3 X + 5 = − 10 Justification: Add X X X To Both Sides.2. 3 X + 5 = − 10 3x + 5 = -10 3 X + 5 = − 10 Step 2: $3x =

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 explore the steps involved in solving linear equations, using the example of Mariena's solution to the equation $2x + 5 = -10 - x$. We will break down each step of her solution and provide a justification for each operation.

Understanding Linear Equations

A linear equation is an equation in which the highest power of the variable (in this case, $x$) is 1. Linear equations can be written in the form $ax + b = c$, where $a$, $b$, and $c$ are constants. The goal of solving a linear equation is to isolate the variable, $x$, on one side of the equation.

Mariena's Solution

Let's take a closer look at Mariena's solution to the equation $2x + 5 = -10 - x$.

Step 1: Add $x$ to both sides

Mariena starts by adding $x$ to both sides of the equation:

$2x + 5 = -10 - x$

$3x + 5 = -10$

Justification: Adding $x$ to both sides is a valid operation because it preserves the equality of the equation. When we add the same value to both sides of an equation, the equation remains true.

Step 2: Subtract 5 from both sides

Mariena then subtracts 5 from both sides of the equation:

$3x + 5 = -10$

$3x = -15$

Justification: Subtracting 5 from both sides is a valid operation because it preserves the equality of the equation. When we subtract the same value from both sides of an equation, the equation remains true.

Step 3: Divide both sides by 3

Finally, Mariena divides both sides of the equation by 3:

$3x = -15$

$x = -5$

Justification: Dividing both sides by 3 is a valid operation because it preserves the equality of the equation. When we divide both sides of an equation by a non-zero value, the equation remains true.

Conclusion

In conclusion, Mariena's solution to the equation $2x + 5 = -10 - x$ is a valid one. By following the steps outlined above, we can see that each operation is justified and preserves the equality of the equation. Solving linear equations is an essential skill for students to master, and by following these steps, we can ensure that our solutions are accurate and reliable.

Tips and Tricks

Here are some tips and tricks to help you solve linear equations like Mariena:

• Check your work: Always check your work by plugging your solution back into the original equation.
• Use inverse operations: Use inverse operations to isolate the variable. For example, if you have a term with a coefficient of 3, you can use the inverse operation of division to isolate the variable.
• Simplify your equation: Simplify your equation by combining like terms and eliminating any unnecessary variables.

Common Mistakes

Here are some common mistakes to avoid when solving linear equations:

• Not checking your work: Failing to check your work can lead to incorrect solutions.
• Not using inverse operations: Failing to use inverse operations can lead to incorrect solutions.
• Not simplifying your equation: Failing to simplify your equation can lead to incorrect solutions.

Real-World Applications

Linear equations have many real-world applications, including:

• Physics: Linear equations are used to describe the motion of objects under constant acceleration.
• Engineering: Linear equations are used to design and optimize systems, such as electrical circuits and mechanical systems.
• Economics: Linear equations are used to model economic systems and make predictions about future trends.

Conclusion

Introduction

In our previous article, we explored the steps involved in solving linear equations, using the example of Mariena's solution to the equation $2x + 5 = -10 - x$. We also provided tips and tricks to help you solve linear equations like Mariena. In this article, we will answer some frequently asked questions about solving linear equations.

Q&A

Q: What is a linear equation?

A: A linear equation is an equation in which the highest power of the variable (in this case, $x$) is 1. Linear equations can be written in the form $ax + b = c$, where $a$, $b$, and $c$ are constants.

Q: How do I solve a linear equation?

A: To solve a linear equation, you need to isolate the variable, $x$, on one side of the equation. You can do this by using inverse operations, such as addition, subtraction, multiplication, and division.

Q: What are inverse operations?

A: Inverse operations are operations that "undo" each other. For example, addition and subtraction are inverse operations, as are multiplication and division.

Q: How do I use inverse operations to solve a linear equation?

A: To use inverse operations to solve a linear equation, you need to identify the operation that was used to create the equation and then use the inverse operation to isolate the variable. For example, if the equation is $2x + 5 = -10 - x$, you can use the inverse operation of addition to isolate the variable.

Q: What is the order of operations?

A: The order of operations is a set of rules that tells you which operations to perform first when solving an equation. The order of operations 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 linear equation?

A: To check your work when solving a linear equation, you need to plug your solution back into the original equation and make sure that it is true. If the equation is true, then your solution is 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 checking your work
• Not using inverse operations
• Not simplifying your equation
• Not following the order of operations

Q: How do I simplify my equation when solving a linear equation?

A: To simplify your equation when solving a linear equation, you need to combine like terms and eliminate any unnecessary variables. For example, if the equation is $2x + 5 = -10 - x$, you can simplify it by combining the like terms $2x$ and $-x$ to get $x$.

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

A: Linear equations have many real-world applications, including:

• Physics: Linear equations are used to describe the motion of objects under constant acceleration.
• Engineering: Linear equations are used to design and optimize systems, such as electrical circuits and mechanical systems.
• Economics: Linear equations are used to model economic systems and make predictions about future trends.

Conclusion

In conclusion, solving linear equations is an essential skill for students to master. By following the steps outlined above and avoiding common mistakes, we can ensure that our solutions are accurate and reliable. Linear equations have many real-world applications, and understanding how to solve them is crucial for success in many fields.