Solve For X X X : − 3 X + 3 = − 7 X − 1 -3x + 3 = -7x - 1 − 3 X + 3 = − 7 X − 1

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, $-3x + 3 = -7x - 1$, and provide a step-by-step guide on how to approach it.

What are Linear Equations?

A linear equation is an equation in which the highest power of the variable(s) is 1. It can be written in the form $ax + b = c$, where $a$, $b$, and $c$ are constants, and $x$ is the variable. Linear equations can be solved using various methods, including algebraic manipulation, graphing, and substitution.

The Equation to Solve

The equation we will be solving is $-3x + 3 = -7x - 1$. This equation is a linear equation in one variable, $x$. Our goal is to isolate the variable $x$ and find its value.

Step 1: Add or Subtract to Isolate the Variable

To solve the equation, we need to isolate the variable $x$. We can start by adding or subtracting the same value to both sides of the equation. In this case, we can add $7x$ to both sides to get:

$$-3x + 3 + 7x = -7x - 1 + 7x$$

This simplifies to:

$$4x + 3 = -1$$

Step 2: Subtract to Isolate the Constant Term

Next, we need to isolate the constant term on one side of the equation. We can do this by subtracting 3 from both sides:

$$4x + 3 - 3 = -1 - 3$$

This simplifies to:

$$4x = -4$$

Step 3: Divide to Solve for the Variable

Finally, we need to solve for the variable $x$. We can do this by dividing both sides of the equation by 4:

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

This simplifies to:

$$x = -1$$

Conclusion

In this article, we solved the linear equation $-3x + 3 = -7x - 1$ using a step-by-step approach. We added or subtracted to isolate the variable, subtracted to isolate the constant term, and divided to solve for the variable. By following these steps, we were able to find the value of $x$, which is $-1$.

Tips and Tricks

• When solving linear equations, it's essential to follow the order of operations (PEMDAS) to ensure that you're performing the operations in the correct order.
• When adding or subtracting the same value to both sides of the equation, make sure to do so on both sides of the equation.
• When dividing both sides of the equation by a value, make sure to do so on both sides of the equation.

Common Mistakes to Avoid

• Not following the order of operations (PEMDAS) when solving linear equations.
• Not adding or subtracting the same value to both sides of the equation.
• Not dividing both sides of the equation by a value.

Real-World Applications

Linear equations have numerous 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

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Introduction

In our previous article, we solved the linear equation $-3x + 3 = -7x - 1$ using a step-by-step approach. In this article, we will provide a Q&A guide to help students understand the concepts and techniques involved in 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. It can be written in the form $ax + b = c$, where $a$, $b$, and $c$ are constants, and $x$ is the variable.

Q: How do I solve a linear equation?

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

Q: What is the order of operations (PEMDAS)?

A: The order of operations (PEMDAS) is a set of rules that tells you which operations to perform first when solving an equation. The acronym PEMDAS stands for:

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 add or subtract the same value to both sides of the equation?

A: To add or subtract the same value to both sides of the equation, you need to perform the operation on both sides of the equation. For example, if you want to add 3 to both sides of the equation, you would write:

$$ax + b + 3 = c + 3$$

Q: How do I divide both sides of the equation by a value?

A: To divide both sides of the equation by a value, you need to perform the division operation on both sides of the equation. For example, if you want to divide both sides of the equation by 2, you would write:

$$\frac{ax + b}{2} = \frac{c}{2}$$

Q: What are some common mistakes to avoid when solving linear equations?

A: Some common mistakes to avoid when solving linear equations include:

• Not following the order of operations (PEMDAS)
• Not adding or subtracting the same value to both sides of the equation
• Not dividing both sides of the equation by a value
• Not isolating the variable

Q: How do I check my answer?

A: To check your answer, you need to plug the value of the variable back into the original equation and see if it is true. For example, if you solved the equation $ax + b = c$ and got $x = 2$, you would plug $x = 2$ back into the original equation to see if it is true.

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

A: Linear equations have numerous 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 a crucial skill for students to master. By following a step-by-step approach and avoiding common mistakes, students can solve linear equations with ease. The Q&A guide provided in this article should help students understand the concepts and techniques involved in solving linear equations.