Solve For { X $} . . . { 3x + 2 = 8 \}

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Introduction

Solving for $x$ in an equation is a fundamental concept in mathematics, and it's essential to understand how to isolate the variable in a linear equation. In this article, we'll focus on solving for $x$ in the equation $3x + 2 = 8$. We'll break down the steps involved in solving this equation and provide a clear explanation of each step.

Understanding the Equation

The given equation is $3x + 2 = 8$. This is a linear equation, which means it can be written in the form $ax + b = c$, where $a$, $b$, and $c$ are constants. In this case, $a = 3$, $b = 2$, and $c = 8$. Our goal is to isolate the variable $x$ and find its value.

Step 1: Subtract 2 from Both Sides

To isolate $x$, we need to get rid of the constant term $2$ that's being added to $3x$. We can do this by subtracting $2$ from both sides of the equation. This will give us:

$$3x + 2 - 2 = 8 - 2$$

Simplifying the equation, we get:

$$3x = 6$$

Step 2: Divide Both Sides by 3

Now that we have $3x$ isolated, we need to get rid of the coefficient $3$ that's being multiplied by $x$. We can do this by dividing both sides of the equation by $3$. This will give us:

$$\frac{3x}{3} = \frac{6}{3}$$

Simplifying the equation, we get:

$$x = 2$$

Conclusion

In this article, we solved for $x$ in the equation $3x + 2 = 8$. We broke down the steps involved in solving this equation and provided a clear explanation of each step. By following these steps, we were able to isolate the variable $x$ and find its value.

Tips and Tricks

• When solving for $x$, it's essential to follow the order of operations (PEMDAS) to ensure that you're performing the correct operations in the correct order.
• When subtracting or adding a constant term to both sides of the equation, make sure to subtract or add the same value to both sides.
• When dividing both sides of the equation by a coefficient, make sure to divide both sides by the same value.

Real-World Applications

Solving for $x$ in an equation has many real-world applications. For example, in physics, you may need to solve for the velocity of an object given its acceleration and time. In finance, you may need to solve for the interest rate on a loan given the principal amount, time, and interest rate. In engineering, you may need to solve for the stress on a material given its Young's modulus and strain.

Common Mistakes

• One common mistake when solving for $x$ is to forget to follow the order of operations (PEMDAS).
• Another common mistake is to subtract or add a constant term to only one side of the equation instead of both sides.
• A third common mistake is to divide both sides of the equation by a coefficient without checking if the coefficient is zero.

Final Thoughts

Solving for $x$ in an equation is a fundamental concept in mathematics, and it's essential to understand how to isolate the variable in a linear equation. By following the steps outlined in this article, you should be able to solve for $x$ in any linear equation. Remember to follow the order of operations (PEMDAS), subtract or add constant terms to both sides of the equation, and divide both sides of the equation by a coefficient only if it's not zero.

Additional Resources

• Khan Academy: Solving Linear Equations
• Mathway: Solving Linear Equations
• Wolfram Alpha: Solving Linear Equations

Glossary

• Linear Equation: An equation in which the highest power of the variable is 1.
• Variable: A symbol or expression that represents a value that can change.
• Coefficient: A number or expression that multiplies a variable.
• Constant Term: A number or expression that is added to or subtracted from a variable.
• Order of Operations (PEMDAS): A set of rules that dictate the order in which operations should be performed when evaluating an expression.
  

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Introduction

In our previous article, we solved for $x$ in the equation $3x + 2 = 8$. We broke down the steps involved in solving this equation and provided a clear explanation of each step. In this article, we'll answer some frequently asked questions (FAQs) related to solving for $x$ in a linear equation.

Q&A

Q: What is the first step in solving for $x$ in a linear equation?

A: The first step in solving for $x$ in a linear equation is to isolate the variable $x$ by getting rid of any constant terms that are being added to or subtracted from it.

Q: How do I isolate the variable $x$ in a linear equation?

A: To isolate the variable $x$, you need to get rid of any constant terms that are being added to or subtracted from it. You can do this by subtracting or adding the same value to both sides of the equation.

Q: What is the order of operations (PEMDAS) and why is it important?

A: The order of operations (PEMDAS) is a set of rules that dictate the order in which operations should be performed when evaluating an expression. It stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction. It's essential to follow the order of operations to ensure that you're performing the correct operations in the correct order.

Q: What is the difference between a coefficient and a constant term?

A: A coefficient is a number or expression that multiplies a variable, while a constant term is a number or expression that is added to or subtracted from a variable.

Q: How do I divide both sides of an equation by a coefficient?

A: When dividing both sides of an equation by a coefficient, make sure to divide both sides by the same value. Also, check if the coefficient is zero before dividing, as dividing by zero is undefined.

Q: What are some common mistakes to avoid when solving for $x$ in a linear equation?

A: Some common mistakes to avoid when solving for $x$ in a linear equation include forgetting to follow the order of operations (PEMDAS), subtracting or adding a constant term to only one side of the equation instead of both sides, and dividing both sides of the equation by a coefficient without checking if the coefficient is zero.

Q: How do I check if my solution is correct?

A: To check if your solution is correct, plug the value of $x$ back into the original equation and simplify. If the equation holds true, then your solution is correct.

Q: What are some real-world applications of solving for $x$ in a linear equation?

A: Solving for $x$ in a linear equation has many real-world applications, including physics, finance, and engineering. For example, in physics, you may need to solve for the velocity of an object given its acceleration and time. In finance, you may need to solve for the interest rate on a loan given the principal amount, time, and interest rate.

Conclusion

Solving for $x$ in a linear equation is a fundamental concept in mathematics, and it's essential to understand how to isolate the variable in a linear equation. By following the steps outlined in this article and avoiding common mistakes, you should be able to solve for $x$ in any linear equation. Remember to follow the order of operations (PEMDAS), subtract or add constant terms to both sides of the equation, and divide both sides of the equation by a coefficient only if it's not zero.

Additional Resources

• Khan Academy: Solving Linear Equations
• Mathway: Solving Linear Equations
• Wolfram Alpha: Solving Linear Equations

Glossary

• Linear Equation: An equation in which the highest power of the variable is 1.
• Variable: A symbol or expression that represents a value that can change.
• Coefficient: A number or expression that multiplies a variable.
• Constant Term: A number or expression that is added to or subtracted from a variable.
• Order of Operations (PEMDAS): A set of rules that dictate the order in which operations should be performed when evaluating an expression.