Solve The Equation And Check Your Answer.$\[ 6(z - 8) = Z \\]$\[ Z = \square \\] (Type An Integer Or A Simplified Fraction.)

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Introduction

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Solving equations is a fundamental concept in mathematics, and it's essential to understand how to approach them. In this article, we will guide you through the process of solving a linear equation and checking your answer. We will use the given equation: $6(z - 8) = z$ and find the value of $z$.

The Given Equation

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The given equation is $6(z - 8) = z$. To solve this equation, we need to isolate the variable $z$ on one side of the equation. We can start by distributing the 6 on the left-hand side of the equation.

Distributing the 6

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When we distribute the 6, we get:

$6(z - 8) = 6z - 48$

So, the equation becomes:

$6z - 48 = z$

Combining Like Terms

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Now, we can combine like terms on the left-hand side of the equation. We have two terms with the variable $z$, so we can combine them.

Combining the $z$ Terms

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When we combine the $z$ terms, we get:

$6z - z = 5z$

So, the equation becomes:

$5z - 48 = z$

Isolating the Variable

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Now, we need to isolate the variable $z$ on one side of the equation. We can do this by adding 48 to both sides of the equation.

Adding 48 to Both Sides

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When we add 48 to both sides of the equation, we get:

$5z - 48 + 48 = z + 48$

Simplifying the equation, we get:

$5z = z + 48$

Subtracting $z$ from Both Sides

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Now, we need to subtract $z$ from both sides of the equation to isolate the variable $z$.

Subtracting $z$ from Both Sides

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When we subtract $z$ from both sides of the equation, we get:

$5z - z = z + 48 - z$

Simplifying the equation, we get:

$4z = 48$

Dividing Both Sides by 4

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Now, we need to divide both sides of the equation by 4 to find the value of $z$.

Dividing Both Sides by 4

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When we divide both sides of the equation by 4, we get:

$\frac{4z}{4} = \frac{48}{4}$

Simplifying the equation, we get:

$z = 12$

Checking the Answer

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Now that we have found the value of $z$, we need to check our answer by plugging it back into the original equation.

Plugging $z = 12$ into the Original Equation

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When we plug $z = 12$ into the original equation, we get:

$6(12 - 8) = 12$

Simplifying the equation, we get:

$6(4) = 12$

$24 = 12$

Since the equation is true, our answer is correct.

Conclusion

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In this article, we have guided you through the process of solving a linear equation and checking your answer. We have used the given equation $6(z - 8) = z$ and found the value of $z$ to be 12. We have also checked our answer by plugging it back into the original equation, and it is true. This demonstrates the importance of checking your answer in mathematics.

Final Answer

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The final answer is $\boxed{12}$.

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Introduction

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In our previous article, we guided you through the process of solving a linear equation and checking your answer. We used the given equation $6(z - 8) = z$ and found the value of $z$ to be 12. In this article, we will answer some frequently asked questions related to solving linear equations and checking your answer.

Q&A

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Q: What is a linear equation?

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A: A linear equation is an equation in which the highest power of the variable(s) is 1. In other words, it is an equation that can be written in the form $ax + b = c$, where $a$, $b$, and $c$ are constants, and $x$ is the variable.

Q: How do I solve a linear equation?

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A: To solve a linear equation, you need to isolate the variable on one side of the equation. You can do this by using inverse operations, such as addition, subtraction, multiplication, and division. For example, if you have the equation $x + 3 = 5$, you can subtract 3 from both sides to get $x = 2$.

Q: What is the difference between a linear equation and a quadratic equation?

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A: A linear equation is an equation in which the highest power of the variable(s) is 1, while a quadratic equation is an equation in which the highest power of the variable(s) is 2. For example, the equation $x^2 + 4x + 4 = 0$ is a quadratic equation, while the equation $x + 3 = 5$ is a linear equation.

Q: How do I check my answer when solving a linear equation?

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A: To check your answer when solving a linear equation, you need to plug your solution back into the original equation and see if it is true. For example, if you have the equation $x + 3 = 5$ and you solve it to get $x = 2$, you can plug $x = 2$ back into the original equation to get $2 + 3 = 5$, which is true.

Q: What are some common mistakes to avoid when solving linear equations?

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A: Some common mistakes to avoid when solving linear equations include:

• Not isolating the variable on one side of the equation
• Not using inverse operations correctly
• Not checking your answer
• Not simplifying the equation

Q: How do I simplify an equation?

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A: To simplify an equation, you need to combine like terms and eliminate any unnecessary operations. For example, if you have the equation $2x + 3x = 5x + 2$, you can combine the like terms to get $5x = 5x + 2$, and then eliminate the unnecessary operation to get $0 = 2$.

Conclusion

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In this article, we have answered some frequently asked questions related to solving linear equations and checking your answer. We have also provided some tips and tricks to help you avoid common mistakes when solving linear equations. By following these tips and practicing regularly, you will become more confident and proficient in solving linear equations.

Final Answer

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The final answer is $\boxed{12}$.