If Y = 87.5 Y = 87.5 Y = 87.5 , What Is The Value Of X X X ?${ \begin{align*} 300x + \frac{500}{7}y &= 10,000 \ 300x + \frac{500}{7}(87.5) &= 10,000 \ 300x + 6,250 &= 10,000 \end{align*} }$

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Introduction

In this article, we will explore how to solve for x in a linear equation. We will use a specific equation as an example to demonstrate the steps involved in solving for x. The equation we will be using is:

300x + 6,250 = 10,000

Understanding the Equation

The equation we are given is a linear equation, which means it is an equation in which the highest power of the variable (in this case, x) is 1. The equation is in the form of:

ax + b = c

where a, b, and c are constants.

In our equation, a = 300, b = 6,250, and c = 10,000.

Solving for x

To solve for x, we need to isolate x on one side of the equation. We can do this by subtracting 6,250 from both sides of the equation.

300x + 6,250 - 6,250 = 10,000 - 6,250

This simplifies to:

300x = 3,750

Isolating x

Now that we have 300x = 3,750, we can isolate x by dividing both sides of the equation by 300.

300x / 300 = 3,750 / 300

This simplifies to:

x = 12.5

Conclusion

In this article, we have demonstrated how to solve for x in a linear equation. We used the equation 300x + 6,250 = 10,000 as an example and showed how to isolate x by subtracting 6,250 from both sides of the equation and then dividing both sides by 300. The value of x is 12.5.

Example Use Cases

Solving for x in a linear equation has many practical applications in mathematics and real-world scenarios. Here are a few examples:

  • Finance: In finance, linear equations are used to calculate interest rates, investment returns, and other financial metrics.
  • Science: In science, linear equations are used to model population growth, chemical reactions, and other phenomena.
  • Engineering: In engineering, linear equations are used to design and optimize systems, such as electrical circuits and mechanical systems.

Tips and Tricks

Here are a few tips and tricks to help you solve for x in a linear equation:

  • Use the distributive property: When multiplying a constant by a variable, use the distributive property to simplify the equation.
  • Combine like terms: When combining like terms, make sure to combine the coefficients of the variable.
  • Check your work: Always check your work by plugging the value of x back into the original equation.

Common Mistakes

Here are a few common mistakes to avoid when solving for x in a linear equation:

  • Forgetting to isolate x: Make sure to isolate x on one side of the equation.
  • Not checking your work: Always check your work by plugging the value of x back into the original equation.
  • Not using the distributive property: Make sure to use the distributive property when multiplying a constant by a variable.

Conclusion

Introduction

In our previous article, we explored how to solve for x in a linear equation. We used a specific equation as an example to demonstrate the steps involved in solving for x. In this article, we will answer some frequently asked questions about solving for x in a linear equation.

Q: What is a linear equation?

A: A linear equation is an equation in which the highest power of the variable (in this case, x) is 1. The equation is in the form of:

ax + b = c

where a, b, and c are constants.

Q: How do I solve for x in a linear equation?

A: To solve for x, you need to isolate x on one side of the equation. You can do this by subtracting b from both sides of the equation and then dividing both sides by a.

Q: What if the equation has fractions?

A: If the equation has fractions, you can eliminate the fractions by multiplying both sides of the equation by the least common multiple (LCM) of the denominators.

Q: What if the equation has decimals?

A: If the equation has decimals, you can eliminate the decimals by multiplying both sides of the equation by a power of 10.

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

A: Yes, you can use a calculator to solve for x. However, make sure to check your work by plugging the value of x back into the original equation.

Q: What if I get a negative value for x?

A: If you get a negative value for x, it means that the equation has no solution. This can happen if the equation is inconsistent or if the coefficients of the variable are negative.

Q: Can I use algebraic methods to solve for x?

A: Yes, you can use algebraic methods to solve for x. Some common algebraic methods include:

  • Substitution method: Substitute the value of one variable into the equation and solve for the other variable.
  • Elimination method: Eliminate one variable by adding or subtracting the equations.
  • Graphing method: Graph the equations on a coordinate plane and find the point of intersection.

Q: What are some common mistakes to avoid when solving for x?

A: Some common mistakes to avoid when solving for x include:

  • Forgetting to isolate x: Make sure to isolate x on one side of the equation.
  • Not checking your work: Always check your work by plugging the value of x back into the original equation.
  • Not using the distributive property: Make sure to use the distributive property when multiplying a constant by a variable.

Q: Can I use technology to solve for x?

A: Yes, you can use technology to solve for x. Some common technologies include:

  • Graphing calculators: Graphing calculators can be used to graph the equations and find the point of intersection.
  • Computer algebra systems: Computer algebra systems can be used to solve for x using algebraic methods.
  • Online calculators: Online calculators can be used to solve for x using algebraic methods or numerical methods.

Conclusion

Solving for x in a linear equation is a fundamental skill in mathematics and has many practical applications in real-world scenarios. By following the steps outlined in this article and avoiding common mistakes, you can become proficient in solving for x in a linear equation.