Solve For \[$ X \$\] In The Equation: $\[ \frac{x}{3} + 11 = 5 \\]

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Introduction

Solving for x in an equation is a fundamental concept in mathematics, and it is essential to understand how to isolate the variable in a given equation. In this article, we will focus on solving for x in the equation x3+11=5\frac{x}{3} + 11 = 5. This equation involves fractions, and we will use algebraic techniques to isolate the variable x.

Understanding the Equation

The given equation is x3+11=5\frac{x}{3} + 11 = 5. To solve for x, we need to isolate the variable x on one side of the equation. The equation involves a fraction, and we will use algebraic techniques to eliminate the fraction.

Step 1: Subtract 11 from Both Sides

To eliminate the constant term 11, we will subtract 11 from both sides of the equation. This will help us to isolate the fraction containing x.

x3+11−11=5−11\frac{x}{3} + 11 - 11 = 5 - 11

Simplifying the equation, we get:

x3=−6\frac{x}{3} = -6

Step 2: Multiply Both Sides by 3

To eliminate the fraction, we will multiply both sides of the equation by 3. This will help us to isolate the variable x.

3×x3=3×−63 \times \frac{x}{3} = 3 \times -6

Simplifying the equation, we get:

x=−18x = -18

Conclusion

In this article, we solved for x in the equation x3+11=5\frac{x}{3} + 11 = 5. We used algebraic techniques to isolate the variable x, and we were able to find the value of x. The final answer is x = -18.

Tips and Tricks

  • When solving for x in an equation involving fractions, it is essential to eliminate the fraction by multiplying both sides of the equation by the denominator.
  • When subtracting a constant term from both sides of the equation, make sure to subtract the same value from both sides.
  • When multiplying both sides of the equation by a value, make sure to multiply both sides by the same value.

Real-World Applications

Solving for x in an equation is a fundamental concept in mathematics, and it has numerous real-world applications. Some of the real-world applications of solving for x include:

  • Physics: Solving for x is essential in physics to calculate the position, velocity, and acceleration of objects.
  • Engineering: Solving for x is essential in engineering to design and optimize systems.
  • Economics: Solving for x is essential in economics to model and analyze economic systems.

Final Thoughts

Solving for x in an equation is a fundamental concept in mathematics, and it is essential to understand how to isolate the variable in a given equation. In this article, we solved for x in the equation x3+11=5\frac{x}{3} + 11 = 5. We used algebraic techniques to isolate the variable x, and we were able to find the value of x. The final answer is x = -18.

Frequently Asked Questions

  • Q: What is the value of x in the equation x3+11=5\frac{x}{3} + 11 = 5? A: The value of x is -18.
  • Q: How do I solve for x in an equation involving fractions? A: To solve for x in an equation involving fractions, eliminate the fraction by multiplying both sides of the equation by the denominator.
  • Q: What are some real-world applications of solving for x? A: Some real-world applications of solving for x include physics, engineering, and economics.

References

  • [1] Algebra for Dummies, by Mary Jane Sterling
  • [2] Mathematics for Engineers, by James Stewart
  • [3] Calculus for Dummies, by Mark Ryan

Introduction

In our previous article, we solved for x in the equation x3+11=5\frac{x}{3} + 11 = 5. We used algebraic techniques to isolate the variable x, and we were able to find the value of x. In this article, we will provide a Q&A section to answer some of the most frequently asked questions about solving for x in an equation.

Q&A

Q: What is the value of x in the equation x3+11=5\frac{x}{3} + 11 = 5?

A: The value of x is -18.

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

A: To solve for x in an equation involving fractions, eliminate the fraction by multiplying both sides of the equation by the denominator. For example, in the equation x3+11=5\frac{x}{3} + 11 = 5, we can multiply both sides by 3 to get rid of the fraction.

Q: What are some real-world applications of solving for x?

A: Some real-world applications of solving for x include physics, engineering, and economics. In physics, solving for x is essential to calculate the position, velocity, and acceleration of objects. In engineering, solving for x is essential to design and optimize systems. In economics, solving for x is essential to model and analyze economic systems.

Q: How do I isolate the variable x in an equation?

A: To isolate the variable x in an equation, you need to get x by itself on one side of the equation. You can do this by adding, subtracting, multiplying, or dividing both sides of the equation by the same value.

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

A: Solving for x and solving for y are both algebraic techniques used to isolate a variable in an equation. The main difference between the two is that solving for x involves isolating the variable x, while solving for y involves isolating the variable y.

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

A: Yes, you can use a calculator to solve for x. However, it's essential to understand the algebraic techniques used to solve for x, as calculators can only provide a numerical answer.

Q: How do I check my answer when solving for x?

A: To check your answer when solving for x, plug the value of x back into the original equation and see if it's true. If the equation is true, then your answer is correct.

Tips and Tricks

  • When solving for x in an equation involving fractions, it's essential to eliminate the fraction by multiplying both sides of the equation by the denominator.
  • When subtracting a constant term from both sides of the equation, make sure to subtract the same value from both sides.
  • When multiplying both sides of the equation by a value, make sure to multiply both sides by the same value.
  • Always check your answer when solving for x by plugging the value of x back into the original equation.

Real-World Examples

  • A physics problem: A car is traveling at a speed of 60 km/h. If it travels for 2 hours, how far will it have traveled?
  • An engineering problem: A company is designing a new bridge. If the bridge is 100 meters long and the wind is blowing at a speed of 10 km/h, how long will it take for the bridge to be blown away?
  • An economics problem: A company is producing a new product. If the cost of production is $100 and the selling price is $150, how much profit will the company make?

Conclusion

Solving for x in an equation is a fundamental concept in mathematics, and it has numerous real-world applications. In this article, we provided a Q&A section to answer some of the most frequently asked questions about solving for x in an equation. We also provided some tips and tricks to help you solve for x, as well as some real-world examples to illustrate the importance of solving for x.

Frequently Asked Questions

  • Q: What is the value of x in the equation x3+11=5\frac{x}{3} + 11 = 5? A: The value of x is -18.
  • Q: How do I solve for x in an equation involving fractions? A: To solve for x in an equation involving fractions, eliminate the fraction by multiplying both sides of the equation by the denominator.
  • Q: What are some real-world applications of solving for x? A: Some real-world applications of solving for x include physics, engineering, and economics.

References

  • [1] Algebra for Dummies, by Mary Jane Sterling
  • [2] Mathematics for Engineers, by James Stewart
  • [3] Calculus for Dummies, by Mark Ryan