Solve $\frac{2}{3} - 4 + \frac{z}{6} = 10$Find The Value Of $z$.

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Introduction

In this article, we will be solving for the value of $z$ in the given equation $\frac{2}{3} - 4 + \frac{z}{6} = 10$. This equation involves fractions and a variable, making it a bit more complex than a simple linear equation. We will use algebraic techniques to isolate the variable $z$ and find its value.

Step 1: Simplify the Equation

The first step in solving this equation is to simplify it by getting rid of the fractions. We can do this by multiplying both sides of the equation by the least common multiple (LCM) of the denominators, which is 6.

\frac{2}{3} - 4 + \frac{z}{6} = 10

Multiply both sides by 6:

6 \times \left(\frac{2}{3} - 4 + \frac{z}{6}\right) = 6 \times 10

This simplifies to:

2 - 24 + z = 60

Step 2: Combine Like Terms

Now that we have simplified the equation, we can combine like terms. In this case, we have a constant term on the left-hand side, which is -22.

-22 + z = 60

Step 3: Isolate the Variable

To isolate the variable $z$, we need to get rid of the constant term on the left-hand side. We can do this by adding 22 to both sides of the equation.

-22 + 22 + z = 60 + 22

This simplifies to:

z = 82

Conclusion

In this article, we solved for the value of $z$ in the equation $\frac{2}{3} - 4 + \frac{z}{6} = 10$. We simplified the equation by getting rid of the fractions, combined like terms, and isolated the variable $z$. The final value of $z$ is 82.

Final Answer

The final answer is $\boxed{82}$.

Why is this Important?

Solving equations like this one is an important skill in mathematics, as it allows us to model real-world problems and make predictions about the behavior of systems. In this case, we were able to find the value of $z$ by using algebraic techniques, which is a fundamental concept in mathematics.

Real-World Applications

This type of equation can be used to model a variety of real-world problems, such as:

• Finance: An equation like this one can be used to model the growth of an investment over time.
• Science: An equation like this one can be used to model the behavior of a physical system, such as the motion of an object.
• Engineering: An equation like this one can be used to model the behavior of a complex system, such as a electrical circuit.

Tips and Tricks

Here are a few tips and tricks that can help you solve equations like this one:

• Simplify the equation: Before you start solving the equation, try to simplify it by getting rid of any fractions or other complex terms.
• Combine like terms: Once you have simplified the equation, try to combine like terms to make it easier to solve.
• Isolate the variable: Finally, try to isolate the variable by getting rid of any constant terms on the left-hand side of the equation.

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Introduction

In our previous article, we solved for the value of $z$ in the equation $\frac{2}{3} - 4 + \frac{z}{6} = 10$. In this article, we will answer some frequently asked questions about solving this type of equation.

Q: What is the least common multiple (LCM) of the denominators?

A: The least common multiple (LCM) of the denominators is the smallest number that both denominators can divide into evenly. In this case, the LCM of 3 and 6 is 6.

Q: Why do we need to multiply both sides of the equation by the LCM?

A: We need to multiply both sides of the equation by the LCM to get rid of the fractions. This makes it easier to solve the equation and isolate the variable $z$.

Q: How do we combine like terms in the equation?

A: To combine like terms, we need to identify the terms that have the same variable and coefficient. In this case, we have a constant term on the left-hand side, which is -22. We can combine this term with the variable $z$ to get a single term.

Q: Why do we need to isolate the variable $z$?

A: We need to isolate the variable $z$ to find its value. By getting rid of the constant term on the left-hand side, we can solve for $z$ and find its value.

Q: What are some real-world applications of solving equations like this one?

A: Solving equations like this one can be used to model a variety of real-world problems, such as:

• Finance: An equation like this one can be used to model the growth of an investment over time.
• Science: An equation like this one can be used to model the behavior of a physical system, such as the motion of an object.
• Engineering: An equation like this one can be used to model the behavior of a complex system, such as a electrical circuit.

Q: What are some tips and tricks for solving equations like this one?

A: Here are a few tips and tricks that can help you solve equations like this one:

• Simplify the equation: Before you start solving the equation, try to simplify it by getting rid of any fractions or other complex terms.
• Combine like terms: Once you have simplified the equation, try to combine like terms to make it easier to solve.
• Isolate the variable: Finally, try to isolate the variable by getting rid of any constant terms on the left-hand side of the equation.

Q: What is the final answer to the equation $\frac{2}{3} - 4 + \frac{z}{6} = 10$?

A: The final answer to the equation $\frac{2}{3} - 4 + \frac{z}{6} = 10$ is $z = 82$.

Conclusion

In this article, we answered some frequently asked questions about solving the equation $\frac{2}{3} - 4 + \frac{z}{6} = 10$. We covered topics such as the least common multiple, combining like terms, and isolating the variable. We also discussed some real-world applications of solving equations like this one and provided some tips and tricks for solving them.