Solve For \[$ X \$\]:$\[ -5x - 5 = -3x + 5 \\]

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Introduction

Solving linear equations is a fundamental concept in mathematics, and it is essential to understand how to isolate variables to find their values. In this discussion, we will focus on solving a linear equation with one variable, $x$. The given equation is $-5x - 5 = -3x + 5$, and our goal is to solve for $x$.

Understanding the Equation

The given equation is a linear equation with one variable, $x$. It is in the form of $ax + b = cx + d$, where $a$, $b$, $c$, and $d$ are constants. In this case, $a = -5$, $b = -5$, $c = -3$, and $d = 5$. Our objective is to isolate the variable $x$ and find its value.

Step 1: Add $3x$ to Both Sides

To solve for $x$, we need to isolate the variable on one side of the equation. We can start by adding $3x$ to both sides of the equation. This will help us to get rid of the negative term on the left-hand side.

$$-5x - 5 + 3x = -3x + 5 + 3x$$

Simplifying the equation, we get:

$$-2x - 5 = 5$$

Step 2: Add $5$ to Both Sides

Next, we need to get rid of the constant term on the left-hand side. We can do this by adding $5$ to both sides of the equation.

$$-2x - 5 + 5 = 5 + 5$$

Simplifying the equation, we get:

$$-2x = 10$$

Step 3: Divide Both Sides by $-2$

Now, we need to isolate the variable $x$ by dividing both sides of the equation by $-2$.

$$\frac{-2x}{-2} = \frac{10}{-2}$$

Simplifying the equation, we get:

$$x = -5$$

Conclusion

In this discussion, we solved a linear equation with one variable, $x$. We started by adding $3x$ to both sides of the equation to get rid of the negative term on the left-hand side. Then, we added $5$ to both sides to get rid of the constant term on the left-hand side. Finally, we divided both sides by $-2$ to isolate the variable $x$. The solution to the equation is $x = -5$.

Example Use Case

Solving linear equations is a fundamental concept in mathematics, and it has numerous applications in real-life situations. For example, in finance, linear equations can be used to calculate interest rates, investment returns, and other financial metrics. In physics, linear equations can be used to describe the motion of objects, calculate forces, and determine energy levels. In engineering, linear equations can be used to design and optimize systems, such as electrical circuits, mechanical systems, and control systems.

Tips and Tricks

When solving linear equations, it is essential to follow the order of operations (PEMDAS) and to isolate the variable on one side of the equation. Additionally, it is crucial to check the solution by plugging it back into the original equation to ensure that it is true.

Common Mistakes

When solving linear equations, some common mistakes include:

• Not following the order of operations (PEMDAS)
• Not isolating the variable on one side of the equation
• Not checking the solution by plugging it back into the original equation
• Making arithmetic errors, such as adding or subtracting the wrong numbers

Conclusion

Solving linear equations is a fundamental concept in mathematics, and it has numerous applications in real-life situations. By following the steps outlined in this discussion, you can solve linear equations with confidence and accuracy. Remember to always follow the order of operations (PEMDAS), isolate the variable on one side of the equation, and check the solution by plugging it back into the original equation.

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Introduction

In our previous discussion, we solved a linear equation with one variable, $x$. We started by adding $3x$ to both sides of the equation to get rid of the negative term on the left-hand side. Then, we added $5$ to both sides to get rid of the constant term on the left-hand side. Finally, we divided both sides by $-2$ to isolate the variable $x$. The solution to the equation is $x = -5$. In this Q&A article, we will answer some common questions 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, it is an equation in which the variable(s) are not raised to any power other than 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, or by multiplying or dividing both sides of the equation by the same non-zero 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 you have multiple operations in an expression. 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 check my solution?

A: To check your solution, plug the value of the variable back into the original equation and simplify. 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 following the order of operations (PEMDAS)
• Not isolating the variable on one side of the equation
• Not checking the solution by plugging it back into the original equation
• Making arithmetic errors, such as adding or subtracting the wrong numbers

Q: Can I use a calculator to solve linear equations?

A: Yes, you can use a calculator to solve linear equations. However, it is still important to understand the steps involved in solving the equation and to check your solution by plugging it back into the original equation.

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

A: To solve a linear equation with fractions, you need to eliminate the fractions by multiplying both sides of the equation by the least common multiple (LCM) of the denominators.

Q: Can I solve a linear equation with decimals?

A: Yes, you can solve a linear equation with decimals. However, it is often easier to convert the decimals to fractions or to use a calculator to solve the equation.

Conclusion

Solving linear equations is a fundamental concept in mathematics, and it has numerous applications in real-life situations. By following the steps outlined in this Q&A article, you can solve linear equations with confidence and accuracy. Remember to always follow the order of operations (PEMDAS), isolate the variable on one side of the equation, and check the solution by plugging it back into the original equation.