Determine If Each Value Is A Solution Of The Equation Z = Z + 3 Z = Z + 3 Z = Z + 3 .${ \begin{array}{|c|c|} \hline \text{Value} & \text{Solution?} \ \hline 0 & ? \ \hline 1 & ? \ \hline 2 & ? \ \hline \end{array} }$

Solving the Equation: Is Each Value a Solution?

In mathematics, an equation is a statement that two expressions are equal. Solving an equation involves finding the values of the variables that make the equation true. In this article, we will explore the equation $z = z + 3$ and determine if each value is a solution to the equation.

Understanding the Equation

The equation $z = z + 3$ is a simple linear equation. It states that the value of $z$ is equal to the value of $z$ plus 3. To solve this equation, we need to find the value of $z$ that makes the equation true.

Subtracting 3 from Both Sides

To solve the equation, we can start by subtracting 3 from both sides. This will give us:

$$z - 3 = z$$

Simplifying the Equation

Now, we can simplify the equation by combining like terms. Since $z$ is on both sides of the equation, we can subtract $z$ from both sides, which gives us:

$$-3 = 0$$

Analyzing the Results

At this point, we have a contradiction. The equation $-3 = 0$ is not true. This means that the original equation $z = z + 3$ has no solution.

Determining if Each Value is a Solution

Now that we have analyzed the equation, we can determine if each value is a solution. We will use the table below to record our results.

Value	Solution?
0	?
1	?
2	?

Analyzing the Value 0

Let's start by analyzing the value 0. We can substitute 0 into the equation $z = z + 3$ and see if it is true.

$$0 = 0 + 3$$

This equation is not true, since 0 is not equal to 3. Therefore, the value 0 is not a solution to the equation.

Analyzing the Value 1

Next, let's analyze the value 1. We can substitute 1 into the equation $z = z + 3$ and see if it is true.

$$1 = 1 + 3$$

This equation is not true, since 1 is not equal to 4. Therefore, the value 1 is not a solution to the equation.

Analyzing the Value 2

Finally, let's analyze the value 2. We can substitute 2 into the equation $z = z + 3$ and see if it is true.

$$2 = 2 + 3$$

This equation is not true, since 2 is not equal to 5. Therefore, the value 2 is not a solution to the equation.

In conclusion, we have analyzed the equation $z = z + 3$ and determined that each value is not a solution. The equation has no solution, since it is a contradiction. This means that there is no value of $z$ that makes the equation true.

Table of Results

Value	Solution?
0	No
1	No
2	No

The equation $z = z + 3$ is a simple linear equation that has no solution. This means that there is no value of $z$ that makes the equation true. In mathematics, an equation is a statement that two expressions are equal. Solving an equation involves finding the values of the variables that make the equation true. In this article, we have explored the equation $z = z + 3$ and determined that each value is not a solution.

Real-World Applications

The equation $z = z + 3$ may seem like a simple equation, but it has real-world applications. For example, in finance, the equation can be used to model the growth of an investment. If the investment grows at a rate of 3% per year, the equation $z = z + 3$ can be used to model the growth of the investment over time.

In conclusion, we have analyzed the equation $z = z + 3$ and determined that each value is not a solution. The equation has no solution, since it is a contradiction. This means that there is no value of $z$ that makes the equation true. In mathematics, an equation is a statement that two expressions are equal. Solving an equation involves finding the values of the variables that make the equation true. In this article, we have explored the equation $z = z + 3$ and determined that each value is not a solution.

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Q: What is the equation $z = z + 3$?

A: The equation $z = z + 3$ is a simple linear equation that states that the value of $z$ is equal to the value of $z$ plus 3.

Q: Is the equation $z = z + 3$ true?

A: No, the equation $z = z + 3$ is not true. This is because subtracting 3 from both sides of the equation gives us $-3 = 0$, which is a contradiction.

Q: What does it mean for an equation to have no solution?

A: When an equation has no solution, it means that there is no value of the variable that makes the equation true. In the case of the equation $z = z + 3$, there is no value of $z$ that makes the equation true.

Q: Can we use the equation $z = z + 3$ to model real-world situations?

A: Yes, the equation $z = z + 3$ can be used to model real-world situations, such as the growth of an investment. However, it's essential to note that the equation has no solution, so it's not a useful model in this case.

Q: How do we determine if a value is a solution to the equation $z = z + 3$?

A: To determine if a value is a solution to the equation $z = z + 3$, we can substitute the value into the equation and see if it is true. If the equation is not true, then the value is not a solution.

Q: What are some common mistakes to avoid when solving the equation $z = z + 3$?

A: Some common mistakes to avoid when solving the equation $z = z + 3$ include:

• Not subtracting 3 from both sides of the equation
• Not simplifying the equation
• Not recognizing that the equation has no solution

Q: Can we use algebraic manipulations to solve the equation $z = z + 3$?

A: Yes, we can use algebraic manipulations to solve the equation $z = z + 3$. However, in this case, the equation has no solution, so algebraic manipulations will not help us find a solution.

Q: Is the equation $z = z + 3$ a linear equation?

A: Yes, the equation $z = z + 3$ is a linear equation. It is a simple linear equation that can be solved using basic algebraic manipulations.

Q: Can we use the equation $z = z + 3$ to model the growth of a population?

A: No, the equation $z = z + 3$ is not a useful model for the growth of a population. This is because the equation has no solution, and it does not accurately represent the growth of a population.

Q: What is the significance of the equation $z = z + 3$ in mathematics?

A: The equation $z = z + 3$ is a simple linear equation that has no solution. This means that it is a useful example in mathematics education, as it helps students understand the concept of a solution to an equation and how to determine if a value is a solution.

Q: Can we use the equation $z = z + 3$ to model the growth of an investment?

A: Yes, the equation $z = z + 3$ can be used to model the growth of an investment. However, it's essential to note that the equation has no solution, so it's not a useful model in this case.

Q: What are some real-world applications of the equation $z = z + 3$?

A: Some real-world applications of the equation $z = z + 3$ include:

• Modeling the growth of an investment
• Modeling the growth of a population
• Understanding the concept of a solution to an equation

Q: Can we use the equation $z = z + 3$ to solve a system of equations?

A: No, the equation $z = z + 3$ is not a useful equation to use when solving a system of equations. This is because the equation has no solution, and it does not accurately represent the relationships between the variables in the system.