Solve For \[$ X \$\].$\[ 4 = \frac{1}{2} \sqrt{x-3} \\]

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Introduction

In this article, we will delve into solving for x in the given equation 4 = (1/2)√(x-3). This equation involves a square root, which can be solved using algebraic manipulations. We will break down the solution step by step, making it easy to understand and follow along.

Understanding the Equation

The given equation is 4 = (1/2)√(x-3). To solve for x, we need to isolate the variable x. The first step is to get rid of the fraction (1/2) by multiplying both sides of the equation by 2.

Step 1: Multiply Both Sides by 2

Multiplying both sides of the equation by 2 gives us:

8 = √(x-3)

Simplifying the Equation

Now that we have 8 = √(x-3), we can simplify the equation by squaring both sides. This will eliminate the square root sign.

Step 2: Square Both Sides

Squaring both sides of the equation gives us:

64 = x - 3

Solving for x

Now that we have 64 = x - 3, we can solve for x by adding 3 to both sides of the equation.

Step 3: Add 3 to Both Sides

Adding 3 to both sides of the equation gives us:

67 = x

Conclusion

In this article, we solved for x in the equation 4 = (1/2)√(x-3). We broke down the solution into three steps: multiplying both sides by 2, squaring both sides, and adding 3 to both sides. By following these steps, we were able to isolate the variable x and find the solution.

Final Answer

The final answer is x = 67.

Additional Tips and Tricks

  • When solving equations with square roots, it's essential to get rid of the square root sign by squaring both sides.
  • Make sure to check your work by plugging the solution back into the original equation.
  • Practice solving equations with square roots to become more comfortable with the process.

Real-World Applications

Solving equations with square roots has many real-world applications, such as:

  • Calculating the area of a square or rectangle
  • Finding the length of a side of a square or rectangle
  • Determining the height of an object
  • Calculating the volume of a cube or rectangular prism

Common Mistakes to Avoid

  • Failing to get rid of the square root sign by squaring both sides
  • Not checking your work by plugging the solution back into the original equation
  • Not following the order of operations (PEMDAS)

Conclusion

Solving for x in the equation 4 = (1/2)√(x-3) requires careful algebraic manipulations. By following the steps outlined in this article, you can isolate the variable x and find the solution. Remember to check your work and practice solving equations with square roots to become more comfortable with the process.

Introduction

In our previous article, we solved for x in the equation 4 = (1/2)√(x-3). We broke down the solution into three steps: multiplying both sides by 2, squaring both sides, and adding 3 to both sides. In this article, we will answer some frequently asked questions about solving for x in this equation.

Q&A

Q: What is the first step in solving for x in the equation 4 = (1/2)√(x-3)?

A: The first step is to get rid of the fraction (1/2) by multiplying both sides of the equation by 2.

Q: Why do we need to square both sides of the equation?

A: We need to square both sides of the equation to eliminate the square root sign. This will allow us to isolate the variable x.

Q: What is the final answer to the equation 4 = (1/2)√(x-3)?

A: The final answer is x = 67.

Q: Can we use a calculator to solve for x in this equation?

A: Yes, we can use a calculator to solve for x in this equation. However, it's essential to check your work by plugging the solution back into the original equation.

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

A: Some common mistakes to avoid include failing to get rid of the square root sign by squaring both sides, not checking your work by plugging the solution back into the original equation, and not following the order of operations (PEMDAS).

Q: How can we apply the concept of solving for x in this equation to real-world problems?

A: We can apply the concept of solving for x in this equation to real-world problems such as calculating the area of a square or rectangle, finding the length of a side of a square or rectangle, determining the height of an object, and calculating the volume of a cube or rectangular prism.

Q: Can we use this equation to solve for x in other types of equations?

A: Yes, we can use this equation to solve for x in other types of equations that involve square roots. However, we need to adjust the equation accordingly to fit the specific problem.

Q: What are some tips for practicing solving for x in this equation?

A: Some tips for practicing solving for x in this equation include:

  • Start with simple equations and gradually move on to more complex ones
  • Practice solving equations with different types of square roots (e.g., √2, √3, etc.)
  • Use online resources or worksheets to practice solving for x in this equation
  • Join a study group or find a study partner to practice solving for x in this equation together

Conclusion

Solving for x in the equation 4 = (1/2)√(x-3) requires careful algebraic manipulations. By following the steps outlined in this article and practicing solving for x in this equation, you can become more comfortable with the process and apply it to real-world problems.

Additional Resources

  • Online resources for practicing solving for x in this equation:
  • Khan Academy: Solving Equations with Square Roots
  • Mathway: Solving Equations with Square Roots
  • IXL: Solving Equations with Square Roots
  • Worksheets for practicing solving for x in this equation:
  • Solving Equations with Square Roots Worksheet
  • Solving Equations with Square Roots Practice Test
  • Study groups or online communities for practicing solving for x in this equation:
  • Math Forum: Solving Equations with Square Roots
  • Reddit: r/learnmath: Solving Equations with Square Roots

Final Answer

The final answer is x = 67.