Solve For { X $} . . . { \frac{x}{3} + 10 = X \}

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Introduction

Solving for xx in an equation is a fundamental concept in mathematics, and it's essential to understand how to isolate the variable in a given equation. In this article, we will focus on solving for xx in the equation x3+10=x\frac{x}{3} + 10 = x. This equation involves fractions and linear terms, and we will use algebraic techniques to isolate the variable.

Understanding the Equation

The given equation is x3+10=x\frac{x}{3} + 10 = x. To solve for xx, we need to isolate the variable on one side of the equation. The equation involves a fraction, which can be challenging to work with. However, we can use algebraic techniques to simplify the equation and isolate the variable.

Step 1: Subtract 10 from Both Sides

The first step in solving the equation is to subtract 10 from both sides. This will help us eliminate the constant term on the left-hand side of the equation.

x3+10−10=x−10\frac{x}{3} + 10 - 10 = x - 10

Simplifying the equation, we get:

x3=x−10\frac{x}{3} = x - 10

Step 2: Multiply Both Sides by 3

To eliminate the fraction, we can multiply both sides of the equation by 3. This will help us get rid of the fraction and simplify the equation.

3×x3=3×(x−10)3 \times \frac{x}{3} = 3 \times (x - 10)

Simplifying the equation, we get:

x=3x−30x = 3x - 30

Step 3: Subtract 3x from Both Sides

The next step is to subtract 3x from both sides of the equation. This will help us isolate the variable on one side of the equation.

x−3x=3x−30−3xx - 3x = 3x - 30 - 3x

Simplifying the equation, we get:

−2x=−30-2x = -30

Step 4: Divide Both Sides by -2

Finally, we can divide both sides of the equation by -2 to solve for xx.

−2x−2=−30−2\frac{-2x}{-2} = \frac{-30}{-2}

Simplifying the equation, we get:

x=15x = 15

Conclusion

In this article, we solved for xx in the equation x3+10=x\frac{x}{3} + 10 = x. We used algebraic techniques to isolate the variable and simplify the equation. The final solution is x=15x = 15. This equation involves fractions and linear terms, and we used algebraic techniques to simplify the equation and isolate the variable.

Tips and Tricks

  • When solving for xx, it's essential to isolate the variable on one side of the equation.
  • Use algebraic techniques such as adding, subtracting, multiplying, and dividing to simplify the equation.
  • Be careful when working with fractions, as they can be challenging to work with.
  • Use the order of operations (PEMDAS) to simplify the equation and avoid errors.

Real-World Applications

Solving for xx in an equation has numerous real-world applications. For example, in physics, we use equations to describe the motion of objects. In economics, we use equations to model the behavior of markets. In engineering, we use equations to design and optimize systems.

Common Mistakes

  • Not isolating the variable on one side of the equation.
  • Not using algebraic techniques to simplify the equation.
  • Not being careful when working with fractions.
  • Not using the order of operations (PEMDAS) to simplify the equation.

Final Thoughts

Solving for xx in an equation is a fundamental concept in mathematics. It's essential to understand how to isolate the variable and simplify the equation. By following the steps outlined in this article, you can solve for xx in any equation involving fractions and linear terms. Remember to be careful when working with fractions and use algebraic techniques to simplify the equation.

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Introduction

In our previous article, we solved for xx in the equation x3+10=x\frac{x}{3} + 10 = x. We used algebraic techniques to isolate the variable and simplify the equation. In this article, we will answer some common questions related to solving for xx in an equation.

Q&A

Q: What is the first step in solving for xx in an equation?

A: The first step in solving for xx in an equation is to isolate the variable on one side of the equation. This can be done by adding, subtracting, multiplying, or dividing both sides of the equation by a constant or a variable.

Q: How do I simplify an equation with fractions?

A: To simplify an equation with fractions, you can multiply both sides of the equation by the denominator of the fraction. This will help you eliminate the fraction and simplify the equation.

Q: What is the order of operations (PEMDAS)?

A: The order of operations (PEMDAS) is a set of rules that tells you which operations to perform first when simplifying an equation. The acronym PEMDAS stands for:

  • Parentheses: Evaluate expressions inside parentheses first.
  • Exponents: Evaluate any exponential expressions next.
  • Multiplication and Division: Evaluate any multiplication and division operations from left to right.
  • Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: How do I solve for xx in an equation with multiple variables?

A: To solve for xx in an equation with multiple variables, you can use algebraic techniques such as substitution or elimination. Substitution involves substituting one variable in terms of another variable, while elimination involves adding or subtracting equations to eliminate one variable.

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, x+2=3x + 2 = 3 is a linear equation. A quadratic equation, on the other hand, is an equation in which the highest power of the variable is 2. For example, x2+2x+1=0x^2 + 2x + 1 = 0 is a quadratic equation.

Q: How do I graph an equation?

A: To graph an equation, you can use a graphing calculator or a computer program. You can also use a coordinate plane to plot points and draw a line.

Tips and Tricks

  • Always isolate the variable on one side of the equation.
  • Use algebraic techniques such as addition, subtraction, multiplication, and division to simplify the equation.
  • Be careful when working with fractions and use the order of operations (PEMDAS) to simplify the equation.
  • Use a graphing calculator or a computer program to graph an equation.

Common Mistakes

  • Not isolating the variable on one side of the equation.
  • Not using algebraic techniques to simplify the equation.
  • Not being careful when working with fractions.
  • Not using the order of operations (PEMDAS) to simplify the equation.

Final Thoughts

Solving for xx in an equation is a fundamental concept in mathematics. By following the steps outlined in this article, you can solve for xx in any equation involving fractions and linear terms. Remember to be careful when working with fractions and use algebraic techniques to simplify the equation.