Solve For \[$ X \$\]:$\[ \frac{1}{2} X = 9 \\]

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Introduction

Solving for a variable in an equation is a fundamental concept in mathematics, and it is essential to understand how to isolate the variable to find its value. In this article, we will focus on solving for $x$ in the equation $\frac{1}{2} x = 9$. This equation is a simple linear equation, and we will use algebraic methods to solve for $x$.

Understanding the Equation

The given equation is $\frac{1}{2} x = 9$. This equation states that the product of $\frac{1}{2}$ and $x$ is equal to 9. To solve for $x$, we need to isolate $x$ on one side of the equation.

Isolating the Variable

To isolate $x$, we can start by multiplying both sides of the equation by 2. This will eliminate the fraction and allow us to solve for $x$. The equation becomes:

$$x = 9 \times 2$$

Solving for $x$

Now that we have the equation $x = 9 \times 2$, we can solve for $x$ by multiplying 9 and 2. This gives us:

$$x = 18$$

Conclusion

In this article, we solved for $x$ in the equation $\frac{1}{2} x = 9$. We started by understanding the equation and then isolated the variable $x$ by multiplying both sides of the equation by 2. Finally, we solved for $x$ by multiplying 9 and 2, which gave us the value of $x$ as 18.

Tips and Tricks

• When solving for a variable, it is essential to isolate the variable on one side of the equation.
• Use algebraic methods such as multiplying or dividing both sides of the equation to eliminate fractions and solve for the variable.
• Always check your work by plugging the solution back into the original equation to ensure that it is true.

Real-World Applications

Solving for a variable is a fundamental concept in mathematics, and it has numerous real-world applications. For example, in physics, solving for a variable can help us understand the motion of objects and the forces acting upon them. In economics, solving for a variable can help us understand the behavior of markets and the impact of different variables on the economy.

Common Mistakes

• Failing to isolate the variable on one side of the equation.
• Not checking the work by plugging the solution back into the original equation.
• Not using algebraic methods to eliminate fractions and solve for the variable.

Practice Problems

• Solve for $x$ in the equation $\frac{3}{4} x = 12$.
• Solve for $y$ in the equation $y = 2x + 5$.
• Solve for $z$ in the equation $z = \frac{1}{3} x - 2$.

Solutions to Practice Problems

• Solve for $x$ in the equation $\frac{3}{4} x = 12$:

$$x = 12 \times \frac{4}{3}$$

$$x = 16$$

• Solve for $y$ in the equation $y = 2x + 5$:

$$y = 2x + 5$$

$$y = 2(3) + 5$$

$$y = 6 + 5$$

$$y = 11$$

• Solve for $z$ in the equation $z = \frac{1}{3} x - 2$:

$$z = \frac{1}{3} x - 2$$

$$z = \frac{1}{3}(6) - 2$$

$$z = 2 - 2$$

$$z = 0$$

Conclusion

Solving for a variable is a fundamental concept in mathematics, and it has numerous real-world applications. In this article, we solved for $x$ in the equation $\frac{1}{2} x = 9$ and provided tips and tricks for solving for a variable. We also provided practice problems and solutions to help readers practice and reinforce their understanding of solving for a variable.

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Introduction

In our previous article, we solved for $x$ in the equation $\frac{1}{2} x = 9$. We also provided tips and tricks for solving for a variable and practice problems to help readers practice and reinforce their understanding of solving for a variable. In this article, we will answer some frequently asked questions (FAQs) related to solving for a variable.

Q&A

Q: What is the first step in solving for a variable?

A: The first step in solving for a variable is to understand the equation and identify the variable that we need to solve for. In the equation $\frac{1}{2} x = 9$, we need to solve for $x$.

Q: How do I isolate the variable on one side of the equation?

A: To isolate the variable on one side of the equation, we can use algebraic methods such as multiplying or dividing both sides of the equation. For example, in the equation $\frac{1}{2} x = 9$, we can multiply both sides of the equation by 2 to eliminate the fraction and solve for $x$.

Q: What is the difference between solving for a variable and solving an equation?

A: Solving for a variable is the process of isolating the variable on one side of the equation, while solving an equation is the process of finding the value of the variable that makes the equation true. In other words, solving for a variable is a step in solving an equation.

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

A: Yes, you can use a calculator to solve for a variable. However, it is essential to understand the algebraic methods and techniques used to solve for a variable, as this will help you to check your work and ensure that your solution is correct.

Q: How do I check my work when solving for a variable?

A: To check your work when solving for a variable, you can plug the solution back into the original equation and verify that it is true. For example, if we solve for $x$ in the equation $\frac{1}{2} x = 9$ and get $x = 18$, we can plug $x = 18$ back into the original equation and verify that it is true.

Q: What are some common mistakes to avoid when solving for a variable?

A: Some common mistakes to avoid when solving for a variable include:

• Failing to isolate the variable on one side of the equation
• Not checking the work by plugging the solution back into the original equation
• Not using algebraic methods to eliminate fractions and solve for the variable

Q: Can I solve for a variable in a quadratic equation?

A: Yes, you can solve for a variable in a quadratic equation. However, quadratic equations can be more complex and may require the use of the quadratic formula or other advanced algebraic techniques.

Q: How do I solve for a variable in a system of equations?

A: To solve for a variable in a system of equations, you can use algebraic methods such as substitution or elimination. For example, if we have two equations $x + y = 3$ and $x - y = 1$, we can use substitution to solve for $x$ and $y$.

Conclusion

In this article, we answered some frequently asked questions (FAQs) related to solving for a variable. We covered topics such as isolating the variable, checking the work, and common mistakes to avoid. We also provided examples and practice problems to help readers practice and reinforce their understanding of solving for a variable.

Practice Problems

• Solve for $x$ in the equation $\frac{3}{4} x = 12$.
• Solve for $y$ in the equation $y = 2x + 5$.
• Solve for $z$ in the equation $z = \frac{1}{3} x - 2$.
• Solve for $x$ and $y$ in the system of equations $x + y = 3$ and $x - y = 1$.

Solutions to Practice Problems

• Solve for $x$ in the equation $\frac{3}{4} x = 12$:

$$x = 12 \times \frac{4}{3}$$

$$x = 16$$

• Solve for $y$ in the equation $y = 2x + 5$:

$$y = 2x + 5$$

$$y = 2(3) + 5$$

$$y = 6 + 5$$

$$y = 11$$

• Solve for $z$ in the equation $z = \frac{1}{3} x - 2$:

$$z = \frac{1}{3} x - 2$$

$$z = \frac{1}{3}(6) - 2$$

$$z = 2 - 2$$

$$z = 0$$

• Solve for $x$ and $y$ in the system of equations $x + y = 3$ and $x - y = 1$:

$$x + y = 3$$

$$x - y = 1$$

Adding the two equations, we get:

$$2x = 4$$

$$x = 2$$

Substituting $x = 2$ into one of the original equations, we get:

$$2 + y = 3$$

$$y = 1$$