Complete The Following: Solve For { X $}$ In The Equation $2 + X = -8$.A. 10 B. 6 C. -10 D. -6

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Introduction

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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 simple linear equation of the form $ax + b = c$, where $a$, $b$, and $c$ are constants. We will use the given equation $2 + x = -8$ as an example to demonstrate the step-by-step process of solving for the variable $x$.

Understanding the Equation

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The given equation is $2 + x = -8$. To solve for $x$, we need to isolate the variable on one side of the equation. In this case, we have a constant term $2$ added to the variable $x$, and the result is equal to $-8$.

Step 1: Subtract 2 from Both Sides

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To isolate the variable $x$, we need to get rid of the constant term $2$ on the left side of the equation. We can do this by subtracting $2$ from both sides of the equation. This will give us:

$$x = -8 - 2$$

Step 2: Simplify the Right Side

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Now that we have subtracted $2$ from both sides, we can simplify the right side of the equation by combining the constants. In this case, we have $-8 - 2 = -10$.

Step 3: Write the Final Solution

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After simplifying the right side, we can write the final solution for the variable $x$. In this case, we have:

$$x = -10$$

Conclusion

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Solving linear equations is a straightforward process that involves isolating the variable on one side of the equation. By following the step-by-step process outlined above, we can solve for the variable $x$ in the given equation $2 + x = -8$. The final solution is $x = -10$.

Frequently Asked Questions

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Q: What is the value of $x$ in the equation $2 + x = -8$?

A: The value of $x$ is $-10$.

Q: How do I solve a linear equation of the form $ax + b = c$?

A: To solve a linear equation of the form $ax + b = c$, you need to isolate the variable $x$ on one side of the equation. You can do this by adding or subtracting the same value to both sides of the equation.

Q: What is the difference between a linear equation and a quadratic equation?

A: A linear equation is an equation of the form $ax + b = c$, where $a$, $b$, and $c$ are constants. A quadratic equation is an equation of the form $ax^2 + bx + c = 0$, where $a$, $b$, and $c$ are constants.

Example Problems

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Problem 1: Solve for $x$ in the equation $3 + x = 5$

A: To solve for $x$, we need to isolate the variable on one side of the equation. We can do this by subtracting $3$ from both sides of the equation. This will give us:

$$x = 5 - 3$$

Simplifying the right side, we get:

$$x = 2$$

Problem 2: Solve for $x$ in the equation $x - 2 = 3$

A: To solve for $x$, we need to isolate the variable on one side of the equation. We can do this by adding $2$ to both sides of the equation. This will give us:

$$x = 3 + 2$$

Simplifying the right side, we get:

$$x = 5$$

Tips and Tricks

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Tip 1: Always check your work

When solving a linear equation, it's essential to check your work by plugging the solution back into the original equation. This will help you ensure that your solution is correct.

Tip 2: Use the correct order of operations

When simplifying the right side of the equation, make sure to follow the correct order of operations (PEMDAS). This will help you avoid errors and ensure that your solution is correct.

Tip 3: Practice, practice, practice

Solving linear equations is a skill that requires practice to develop. Make sure to practice solving different types of linear equations to become proficient in this area.

Conclusion

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Solving linear equations is a fundamental skill in mathematics that requires practice to develop. By following the step-by-step process outlined above, you can solve for the variable $x$ in a given equation. Remember to always check your work, use the correct order of operations, and practice solving different types of linear equations to become proficient in this area.

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Introduction

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Linear equations are a fundamental concept in mathematics, and solving them is a crucial skill for students to master. In this article, we will answer some frequently asked questions about linear equations, providing a comprehensive guide to help students understand and solve these types of equations.

Q&A

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Q: What is a linear equation?

A: A linear equation is an equation of the form $ax + b = c$, where $a$, $b$, and $c$ are constants. In other words, it is an equation in which the highest power of the variable is 1.

Q: How do I solve a linear equation?

A: To solve a linear equation, you need to isolate the variable on one side of the equation. You can do this by adding or subtracting the same value to both sides of the equation.

Q: What is the difference between a linear equation and a quadratic equation?

A: A linear equation is an equation of the form $ax + b = c$, where $a$, $b$, and $c$ are constants. A quadratic equation is an equation of the form $ax^2 + bx + c = 0$, where $a$, $b$, and $c$ are constants.

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

A: To check your work, plug the solution back into the original equation. If the solution is correct, the equation should be true. If the solution is incorrect, the equation should be false.

Q: What is the order of operations when simplifying the right side of a linear equation?

A: The order of operations is PEMDAS: Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.

Q: How do I solve a linear equation with fractions?

A: To solve a linear equation with fractions, multiply both sides of the equation by the least common multiple (LCM) of the denominators.

Q: What is the difference between a linear equation and a system of linear equations?

A: A linear equation is an equation of the form $ax + b = c$, where $a$, $b$, and $c$ are constants. A system of linear equations is a set of two or more linear equations that are solved simultaneously.

Q: How do I solve a system of linear equations?

A: To solve a system of linear equations, use the method of substitution or elimination to find the values of the variables.

Q: What is the importance of linear equations in real-life applications?

A: Linear equations are used in a wide range of real-life applications, including physics, engineering, economics, and computer science.

Example Problems

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Problem 1: Solve for $x$ in the equation $2x + 3 = 5$

A: To solve for $x$, we need to isolate the variable on one side of the equation. We can do this by subtracting 3 from both sides of the equation. This will give us:

$$2x = 5 - 3$$

Simplifying the right side, we get:

$$2x = 2$$

Dividing both sides by 2, we get:

$$x = 1$$

Problem 2: Solve for $x$ in the equation $x - 2 = 3$

A: To solve for $x$, we need to isolate the variable on one side of the equation. We can do this by adding 2 to both sides of the equation. This will give us:

$$x = 3 + 2$$

Simplifying the right side, we get:

$$x = 5$$

Tips and Tricks

---

Tip 1: Always check your work

When solving a linear equation, it's essential to check your work by plugging the solution back into the original equation. This will help you ensure that your solution is correct.

Tip 2: Use the correct order of operations

When simplifying the right side of the equation, make sure to follow the correct order of operations (PEMDAS). This will help you avoid errors and ensure that your solution is correct.

Tip 3: Practice, practice, practice

Solving linear equations is a skill that requires practice to develop. Make sure to practice solving different types of linear equations to become proficient in this area.

Conclusion

---

Linear equations are a fundamental concept in mathematics, and solving them is a crucial skill for students to master. By following the step-by-step process outlined above, you can solve for the variable $x$ in a given equation. Remember to always check your work, use the correct order of operations, and practice solving different types of linear equations to become proficient in this area.