Solve For $x$.$8x - 10y = 4$

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Introduction

Solving for $x$ in a linear equation is a fundamental concept in algebra. It involves isolating the variable $x$ on one side of the equation, while keeping the other variables on the other side. In this article, we will focus on solving for $x$ in the equation $8x - 10y = 4$. We will use various algebraic techniques to isolate $x$ and provide a step-by-step solution.

Understanding the Equation

The given equation is $8x - 10y = 4$. This is a linear equation in two variables, $x$ and $y$. The coefficients of $x$ and $y$ are $8$ and $-10$, respectively. The constant term is $4$. To solve for $x$, we need to isolate $x$ on one side of the equation.

Isolating $x$

To isolate $x$, we can start by adding $10y$ to both sides of the equation. This will eliminate the term $-10y$ and allow us to focus on the term $8x$. The equation becomes:

$$8x = 4 + 10y$$

Simplifying the Equation

Next, we can simplify the equation by combining the constant terms on the right-hand side. We can add $4$ and $10y$ to get:

$$8x = 4 + 10y$$

$$8x = 4(1 + 2.5y)$$

Isolating $x$ Further

Now, we can divide both sides of the equation by $8$ to isolate $x$. This will give us:

$$x = \frac{4(1 + 2.5y)}{8}$$

$$x = \frac{1}{2}(1 + 2.5y)$$

Simplifying the Expression

Finally, we can simplify the expression for $x$ by combining the terms inside the parentheses. We can multiply $1$ and $2.5y$ to get:

$$x = \frac{1}{2}(1 + 2.5y)$$

$$x = \frac{1}{2} + \frac{2.5y}{2}$$

$$x = \frac{1}{2} + \frac{5y}{4}$$

Conclusion

In this article, we have solved for $x$ in the equation $8x - 10y = 4$. We have used various algebraic techniques to isolate $x$ and provide a step-by-step solution. The final expression for $x$ is:

$$x = \frac{1}{2} + \frac{5y}{4}$$

This expression shows that $x$ is dependent on the value of $y$. As $y$ changes, $x$ will also change accordingly.

Applications of Solving for $x$

Solving for $x$ has many practical applications in various fields, including physics, engineering, and economics. For example, in physics, solving for $x$ can help us determine the position of an object in a given time. In engineering, solving for $x$ can help us design and optimize systems. In economics, solving for $x$ can help us understand the behavior of markets and make informed decisions.

Tips and Tricks for Solving for $x$

Here are some tips and tricks for solving for $x$:

• Use algebraic techniques: Algebraic techniques such as addition, subtraction, multiplication, and division can help us isolate $x$.
• Simplify the equation: Simplifying the equation can help us identify the terms that need to be isolated.
• Use inverse operations: Inverse operations such as addition and subtraction, multiplication and division can help us isolate $x$.
• Check your work: Checking your work can help you ensure that your solution is correct.

Common Mistakes to Avoid

Here are some common mistakes to avoid when solving for $x$:

• Not simplifying the equation: Failing to simplify the equation can make it difficult to isolate $x$.
• Not using inverse operations: Failing to use inverse operations can make it difficult to isolate $x$.
• Not checking your work: Failing to check your work can lead to incorrect solutions.

Conclusion

Solving for $x$ is a fundamental concept in algebra. It involves isolating the variable $x$ on one side of the equation, while keeping the other variables on the other side. In this article, we have solved for $x$ in the equation $8x - 10y = 4$. We have used various algebraic techniques to isolate $x$ and provide a step-by-step solution. The final expression for $x$ is:

$$x = \frac{1}{2} + \frac{5y}{4}$$

This expression shows that $x$ is dependent on the value of $y$. As $y$ changes, $x$ will also change accordingly.

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Introduction

In our previous article, we solved for $x$ in the equation $8x - 10y = 4$. We used various algebraic techniques to isolate $x$ and provide a step-by-step solution. In this article, we will answer some frequently asked questions (FAQs) related to solving for $x$.

Q&A

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

A: The first step in solving for $x$ is to simplify the equation by combining like terms. This will help us identify the terms that need to be isolated.

Q: How do I isolate $x$ in an equation with multiple variables?

A: To isolate $x$ in an equation with multiple variables, we can use algebraic techniques such as addition, subtraction, multiplication, and division. We can also use inverse operations such as addition and subtraction, multiplication and division to isolate $x$.

Q: What is the difference between solving for $x$ and solving for $y$?

A: Solving for $x$ involves isolating the variable $x$ on one side of the equation, while keeping the other variables on the other side. Solving for $y$ involves isolating the variable $y$ on one side of the equation, while keeping the other variables on the other side.

Q: Can I use a calculator to solve for $x$?

A: Yes, you can use a calculator to solve for $x$. However, it's always a good idea to check your work by hand to ensure that your solution is correct.

Q: What if I have a system of equations with multiple variables?

A: If you have a system of equations with multiple variables, you can use substitution or elimination methods to solve for the variables. Substitution involves solving one equation for one variable and then substituting that expression into the other equation. Elimination involves adding or subtracting the equations to eliminate one or more variables.

Q: Can I use algebraic techniques to solve for $x$ in a quadratic equation?

A: Yes, you can use algebraic techniques to solve for $x$ in a quadratic equation. However, quadratic equations can be more challenging to solve than linear equations, and may require the use of the quadratic formula.

Q: What if I have a rational equation with multiple variables?

A: If you have a rational equation with multiple variables, you can use algebraic techniques such as cross-multiplication and simplification to solve for the variables.

Q: Can I use algebraic techniques to solve for $x$ in a system of equations with multiple variables and multiple equations?

A: Yes, you can use algebraic techniques such as substitution and elimination to solve for the variables in a system of equations with multiple variables and multiple equations.

Tips and Tricks

Here are some tips and tricks for solving for $x$:

• Use algebraic techniques: Algebraic techniques such as addition, subtraction, multiplication, and division can help you isolate $x$.
• Simplify the equation: Simplifying the equation can help you identify the terms that need to be isolated.
• Use inverse operations: Inverse operations such as addition and subtraction, multiplication and division can help you isolate $x$.
• Check your work: Checking your work can help you ensure that your solution is correct.

Common Mistakes to Avoid

Here are some common mistakes to avoid when solving for $x$:

• Not simplifying the equation: Failing to simplify the equation can make it difficult to isolate $x$.
• Not using inverse operations: Failing to use inverse operations can make it difficult to isolate $x$.
• Not checking your work: Failing to check your work can lead to incorrect solutions.

Conclusion

Solving for $x$ is a fundamental concept in algebra. It involves isolating the variable $x$ on one side of the equation, while keeping the other variables on the other side. In this article, we have answered some frequently asked questions (FAQs) related to solving for $x$. We have also provided some tips and tricks for solving for $x$, as well as some common mistakes to avoid.