Solve For { X $} : : : { -\frac{1}{2} X = -10 \}

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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 $-\frac{1}{2} x = -10$. This equation is a simple linear equation, and we will use algebraic methods to solve for $x$.

Understanding the Equation

The given equation is $-\frac{1}{2} x = -10$. This equation is a linear equation, and it can be solved using algebraic methods. The equation is in the form of $ax = b$, where $a$ is the coefficient of $x$ and $b$ is the constant term. In this case, $a = -\frac{1}{2}$ and $b = -10$.

Isolating the Variable

To solve for $x$, we need to isolate the variable on one side of the equation. We can do this by multiplying both sides of the equation by the reciprocal of the coefficient of $x$. In this case, the reciprocal of $-\frac{1}{2}$ is $-2$. Therefore, we can multiply both sides of the equation by $-2$ to isolate $x$.

Solving for $x$

To solve for $x$, we multiply both sides of the equation by $-2$:

$$-\frac{1}{2} x = -10$$

$$\Rightarrow -2 \times -\frac{1}{2} x = -2 \times -10$$

$$\Rightarrow x = 20$$

Therefore, the solution to the equation $-\frac{1}{2} x = -10$ is $x = 20$.

Checking the Solution

To verify that the solution is correct, we can substitute $x = 20$ back into the original equation:

$$-\frac{1}{2} x = -10$$

$$\Rightarrow -\frac{1}{2} \times 20 = -10$$

$$\Rightarrow -10 = -10$$

Since the equation is true, we can conclude that the solution $x = 20$ is correct.

Conclusion

In this article, we solved for $x$ in the equation $-\frac{1}{2} x = -10$. We used algebraic methods to isolate the variable on one side of the equation and found that the solution is $x = 20$. We also verified that the solution is correct by substituting it back into the original equation.

Frequently Asked Questions

• What is the solution to the equation $-\frac{1}{2} x = -10$?
• How do you solve for $x$ in a linear equation?
• What is the reciprocal of a fraction?

Answers

• The solution to the equation $-\frac{1}{2} x = -10$ is $x = 20$.
• To solve for $x$ in a linear equation, you need to isolate the variable on one side of the equation by multiplying both sides by the reciprocal of the coefficient of $x$.
• The reciprocal of a fraction is obtained by swapping the numerator and denominator.

Additional Resources

• For more information on solving linear equations, see the article "Solving Linear Equations".
• For more information on algebraic methods, see the article "Algebraic Methods for Solving Equations".
• For more information on fractions, see the article "Fractions: A Comprehensive Guide".

Related Topics

• Solving Quadratic Equations
• Solving Polynomial Equations
• Algebraic Methods for Solving Equations

References

• [1] "Algebra" by Michael Artin
• [2] "Linear Algebra" by Jim Hefferon
• [3] "Mathematics for Computer Science" by Eric Lehman and Tom Leighton
  

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Introduction

In our previous article, we solved for $x$ in the equation $-\frac{1}{2} x = -10$. In this article, we will answer some frequently asked questions related to solving for $x$ in linear equations.

Q&A

Q: What is the solution to the equation $-\frac{1}{2} x = -10$?

A: The solution to the equation $-\frac{1}{2} x = -10$ is $x = 20$.

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

A: To solve for $x$ in a linear equation, you need to isolate the variable on one side of the equation by multiplying both sides by the reciprocal of the coefficient of $x$.

Q: What is the reciprocal of a fraction?

A: The reciprocal of a fraction is obtained by swapping the numerator and denominator.

Q: Can you explain the concept of isolating the variable?

A: Yes, isolating the variable means getting the variable alone on one side of the equation. This is done by performing operations on both sides of the equation to eliminate the coefficient of the variable.

Q: How do you check if the solution is correct?

A: To check if the solution is correct, you can substitute the solution back into the original equation and verify that it is true.

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

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

• Not isolating the variable on one side of the equation
• Not using the correct reciprocal of the coefficient of $x$
• Not checking if the solution is correct

Q: Can you provide an example of a linear equation with a variable on both sides?

A: Yes, an example of a linear equation with a variable on both sides is:

$$2x + 3 = 5x - 2$$

To solve for $x$, you would need to isolate the variable on one side of the equation.

Q: How do you solve for $x$ in an equation with a variable on both sides?

A: To solve for $x$ in an equation with a variable on both sides, you would need to isolate the variable on one side of the equation by performing operations on both sides of the equation.

Conclusion

In this article, we answered some frequently asked questions related to solving for $x$ in linear equations. We covered topics such as isolating the variable, checking if the solution is correct, and common mistakes to avoid.

Frequently Asked Questions

• What is the solution to the equation $2x + 3 = 5x - 2$?
• How do you solve for $x$ in an equation with a variable on both sides?
• What are some common mistakes to avoid when solving for $x$?

Answers

• The solution to the equation $2x + 3 = 5x - 2$ is $x = 1$.
• To solve for $x$ in an equation with a variable on both sides, you would need to isolate the variable on one side of the equation by performing operations on both sides of the equation.
• Some common mistakes to avoid when solving for $x$ include not isolating the variable on one side of the equation, not using the correct reciprocal of the coefficient of $x$, and not checking if the solution is correct.

Additional Resources

• For more information on solving linear equations, see the article "Solving Linear Equations".
• For more information on algebraic methods, see the article "Algebraic Methods for Solving Equations".
• For more information on fractions, see the article "Fractions: A Comprehensive Guide".

Related Topics

• Solving Quadratic Equations
• Solving Polynomial Equations
• Algebraic Methods for Solving Equations

References

• [1] "Algebra" by Michael Artin
• [2] "Linear Algebra" by Jim Hefferon
• [3] "Mathematics for Computer Science" by Eric Lehman and Tom Leighton