Solve For Z Z Z In The Equation: 15 ( 1 3 ) Z = 5 15\left(\frac{1}{3}\right) Z = 5 15 ( 3 1 ​ ) Z = 5 Z = ? Z = \, ? Z = ?

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Introduction

Solving for $z$ in the given equation involves isolating the variable $z$ on one side of the equation. This requires a step-by-step approach to simplify the equation and ultimately find the value of $z$. In this article, we will guide you through the process of solving for $z$ in the equation $15\left(\frac{1}{3}\right) z = 5$.

Understanding the Equation

The given equation is $15\left(\frac{1}{3}\right) z = 5$. To solve for $z$, we need to isolate the variable $z$ on one side of the equation. The first step is to simplify the left-hand side of the equation by multiplying $15$ and $\frac{1}{3}$.

Simplifying the Left-Hand Side

To simplify the left-hand side of the equation, we multiply $15$ and $\frac{1}{3}$. This can be done by multiplying the numerators and denominators separately.

$$15\left(\frac{1}{3}\right) = \frac{15 \times 1}{3 \times 1} = \frac{15}{3} = 5$$

Now that we have simplified the left-hand side of the equation, we can rewrite the equation as:

$$5z = 5$$

Isolating the Variable $z$

To isolate the variable $z$, we need to get rid of the coefficient $5$ that is multiplied by $z$. This can be done by dividing both sides of the equation by $5$.

$$\frac{5z}{5} = \frac{5}{5}$$

Simplifying the left-hand side of the equation, we get:

$$z = 1$$

Conclusion

In this article, we solved for $z$ in the equation $15\left(\frac{1}{3}\right) z = 5$. We simplified the left-hand side of the equation by multiplying $15$ and $\frac{1}{3}$, and then isolated the variable $z$ by dividing both sides of the equation by $5$. The final value of $z$ is $1$.

Tips and Tricks

• When solving for a variable, always isolate the variable on one side of the equation.
• Simplify the left-hand side of the equation by combining like terms.
• Use inverse operations to isolate the variable.
• Check your solution by plugging it back into the original equation.

Real-World Applications

Solving for a variable is a fundamental concept in mathematics that 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 relationships between different economic variables and make informed decisions.

Common Mistakes

• Failing to isolate the variable on one side of the equation.
• Not simplifying the left-hand side of the equation.
• Using the wrong inverse operation to isolate the variable.

Final Thoughts

Solving for a variable is a crucial skill in mathematics that requires practice and patience. By following the steps outlined in this article, you can develop the skills necessary to solve for a variable and apply them to real-world problems.

Additional Resources

• Khan Academy: Solving Linear Equations
• Mathway: Solving Linear Equations
• Wolfram Alpha: Solving Linear Equations

Frequently Asked Questions

• Q: How do I solve for a variable in a linear equation? A: To solve for a variable in a linear equation, isolate the variable on one side of the equation by using inverse operations.
• Q: What is the first step in solving for a variable? A: The first step in solving for a variable is to simplify the left-hand side of the equation by combining like terms.
• Q: How do I check my solution? A: To check your solution, plug it back into the original equation and verify that it is true.
  

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Introduction

In our previous article, we solved for $z$ in the equation $15\left(\frac{1}{3}\right) z = 5$. We simplified the left-hand side of the equation by multiplying $15$ and $\frac{1}{3}$, and then isolated the variable $z$ by dividing both sides of the equation by $5$. In this article, we will answer some frequently asked questions about solving for $z$ in the equation $15\left(\frac{1}{3}\right) z = 5$.

Q&A

Q: What is the first step in solving for $z$ in the equation $15\left(\frac{1}{3}\right) z = 5$?

A: The first step in solving for $z$ in the equation $15\left(\frac{1}{3}\right) z = 5$ is to simplify the left-hand side of the equation by multiplying $15$ and $\frac{1}{3}$.

Q: How do I simplify the left-hand side of the equation?

A: To simplify the left-hand side of the equation, multiply the numerators and denominators separately. In this case, we have:

$$15\left(\frac{1}{3}\right) = \frac{15 \times 1}{3 \times 1} = \frac{15}{3} = 5$$

Q: What is the next step in solving for $z$?

A: After simplifying the left-hand side of the equation, the next step is to isolate the variable $z$ by dividing both sides of the equation by $5$.

Q: How do I check my solution?

A: To check your solution, plug it back into the original equation and verify that it is true. In this case, we have:

$$5z = 5$$

If we substitute $z = 1$ into the equation, we get:

$$5(1) = 5$$

Which is true.

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

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

• Failing to isolate the variable $z$ on one side of the equation.
• Not simplifying the left-hand side of the equation.
• Using the wrong inverse operation to isolate the variable $z$.

Q: How do I apply the concept of solving for $z$ to real-world problems?

A: The concept of solving for $z$ can be applied to real-world problems in a variety of ways. 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 relationships between different economic variables and make informed decisions.

Tips and Tricks

• Always isolate the variable on one side of the equation.
• Simplify the left-hand side of the equation by combining like terms.
• Use inverse operations to isolate the variable.
• Check your solution by plugging it back into the original equation.

Real-World Applications

Solving for a variable is a fundamental concept in mathematics that 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 relationships between different economic variables and make informed decisions.

Common Mistakes

• Failing to isolate the variable on one side of the equation.
• Not simplifying the left-hand side of the equation.
• Using the wrong inverse operation to isolate the variable.

Final Thoughts

Solving for a variable is a crucial skill in mathematics that requires practice and patience. By following the steps outlined in this article, you can develop the skills necessary to solve for a variable and apply them to real-world problems.

Additional Resources

• Khan Academy: Solving Linear Equations
• Mathway: Solving Linear Equations
• Wolfram Alpha: Solving Linear Equations

Frequently Asked Questions

• Q: How do I solve for a variable in a linear equation? A: To solve for a variable in a linear equation, isolate the variable on one side of the equation by using inverse operations.
• Q: What is the first step in solving for a variable? A: The first step in solving for a variable is to simplify the left-hand side of the equation by combining like terms.
• Q: How do I check my solution? A: To check your solution, plug it back into the original equation and verify that it is true.

Conclusion

In this article, we answered some frequently asked questions about solving for $z$ in the equation $15\left(\frac{1}{3}\right) z = 5$. We also provided some tips and tricks for solving for a variable, as well as some real-world applications of the concept. By following the steps outlined in this article, you can develop the skills necessary to solve for a variable and apply them to real-world problems.