Solve For X.${4x = 64}$

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Introduction

Solving for x in a linear equation is a fundamental concept in mathematics. It involves isolating the variable x on one side of the equation, while the constant term is on the other side. In this article, we will focus on solving for x in the equation 4x = 64. This equation is a simple linear equation, and we will use algebraic methods to solve for x.

Understanding the Equation

The given equation is 4x = 64. This equation states that 4 times x is equal to 64. To solve for x, we need to isolate x on one side of the equation. We can do this by using the inverse operation of multiplication, which is division.

Solving for x

To solve for x, we need to divide both sides of the equation by 4. This will isolate x on one side of the equation. The equation becomes:

4x4=644{ \frac{4x}{4} = \frac{64}{4} }

Using the rule of division, we can simplify the equation as follows:

x=644{ x = \frac{64}{4} }

Simplifying the Equation

To simplify the equation, we can divide 64 by 4. This will give us the value of x.

x=16{ x = 16 }

Conclusion

In this article, we solved for x in the equation 4x = 64. We used algebraic methods to isolate x on one side of the equation. The solution to the equation is x = 16. This is a simple linear equation, and solving for x is a fundamental concept in mathematics.

Real-World Applications

Solving for x in a linear equation has many real-world applications. For example, in finance, solving for x can help us calculate the future value of an investment. In science, solving for x can help us calculate the rate of change of a physical quantity. In engineering, solving for x can help us design and optimize systems.

Tips and Tricks

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

  • Use the inverse operation of multiplication, which is division, to isolate x on one side of the equation.
  • Simplify the equation by dividing both sides of the equation by the coefficient of x.
  • Check your solution by plugging it back into the original equation.

Common Mistakes

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

  • Not isolating x on one side of the equation.
  • Not simplifying the equation.
  • Not checking the solution.

Practice Problems

Here are some practice problems to help you practice solving for x in a linear equation:

  • 2x = 32
  • 5x = 25
  • 3x = 9

Solutions

Here are the solutions to the practice problems:

  • 2x = 32 → x = 16
  • 5x = 25 → x = 5
  • 3x = 9 → x = 3

Conclusion

Solving for x in a linear equation is a fundamental concept in mathematics. It involves isolating the variable x on one side of the equation, while the constant term is on the other side. In this article, we solved for x in the equation 4x = 64. We used algebraic methods to isolate x on one side of the equation. The solution to the equation is x = 16. This is a simple linear equation, and solving for x is a fundamental concept in mathematics.

Final Thoughts

Solving for x in a linear equation has many real-world applications. It is a fundamental concept in mathematics, and it is used in many fields, including finance, science, and engineering. By following the tips and tricks outlined in this article, you can become proficient in solving for x in a linear equation.

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Introduction

In our previous article, we solved for x in the equation 4x = 64. We used algebraic methods to isolate x on one side of the equation. In this article, we will answer some frequently asked questions about 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 x on one side of the equation. This can be done by using the inverse operation of multiplication, which is division.

Q: How do I simplify the equation after isolating x?

A: After isolating x, you can simplify the equation by dividing both sides of the equation by the coefficient of x. This will give you the value of x.

Q: What is the difference between a linear equation and a quadratic equation?

A: A linear equation is an equation in which the highest power of the variable is 1. For example, 2x = 4 is a linear equation. A quadratic equation is an equation in which the highest power of the variable is 2. For example, x^2 + 4x + 4 = 0 is a quadratic equation.

Q: How do I check my solution to a linear equation?

A: To check your solution to a linear equation, you can plug it back into the original equation. If the solution satisfies the equation, then it is the correct solution.

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 not isolating x on one side of the equation, not simplifying the equation, and not checking the solution.

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

A: Yes, you can use a calculator to solve for x in a linear equation. However, it is always a good idea to check your solution by plugging it back into the original equation.

Q: How do I solve for x in an equation with fractions?

A: To solve for x in an equation with fractions, you can multiply both sides of the equation by the least common multiple of the denominators. This will eliminate the fractions and allow you to solve for x.

Q: Can I solve for x in an equation with decimals?

A: Yes, you can solve for x in an equation with decimals. However, it is always a good idea to round the decimals to the nearest whole number to make the calculation easier.

Practice Problems

Here are some practice problems to help you practice solving for x in a linear equation:

  • 2x = 32
  • 5x = 25
  • 3x = 9
  • x/2 = 4
  • 2x + 3 = 7

Solutions

Here are the solutions to the practice problems:

  • 2x = 32 → x = 16
  • 5x = 25 → x = 5
  • 3x = 9 → x = 3
  • x/2 = 4 → x = 8
  • 2x + 3 = 7 → x = 2

Conclusion

Solving for x in a linear equation is a fundamental concept in mathematics. It involves isolating the variable x on one side of the equation, while the constant term is on the other side. In this article, we answered some frequently asked questions about solving for x in a linear equation. We also provided some practice problems to help you practice solving for x in a linear equation.

Final Thoughts

Solving for x in a linear equation has many real-world applications. It is a fundamental concept in mathematics, and it is used in many fields, including finance, science, and engineering. By following the tips and tricks outlined in this article, you can become proficient in solving for x in a linear equation.