Solve For X X X When G ( X ) = − 6 G(x) = -6 G ( X ) = − 6 Given The Function Below: G ( X ) = − − 1 + X 4 G(x) = -\frac{-1 + X}{4} G ( X ) = − 4 − 1 + X ​ Show Your Work Here.

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Introduction

In this article, we will explore how to solve for $x$ in the given function $g(x) = -\frac{-1 + x}{4}$ when $g(x) = -6$. This involves substituting the value of $g(x)$ into the function and solving for $x$. We will break down the steps involved in solving this problem and provide a clear explanation of each step.

Step 1: Substitute the Value of $g(x)$ into the Function

To solve for $x$, we need to substitute the value of $g(x)$ into the function. In this case, we are given that $g(x) = -6$. So, we will substitute $-6$ for $g(x)$ in the function.

Step 2: Simplify the Equation

After substituting the value of $g(x)$ into the function, we will simplify the equation to isolate $x$. This involves multiplying both sides of the equation by the denominator and then solving for $x$.

Step 3: Solve for $x$

Once we have simplified the equation, we will solve for $x$. This involves isolating $x$ on one side of the equation and then solving for its value.

Step 4: Check the Solution

After solving for $x$, we will check our solution to make sure it is correct. This involves plugging the value of $x$ back into the original equation to see if it is true.

Step 5: Conclusion

In this article, we have solved for $x$ in the function $g(x) = -\frac{-1 + x}{4}$ when $g(x) = -6$. We have broken down the steps involved in solving this problem and provided a clear explanation of each step.

Solving the Equation

To solve the equation, we will start by substituting the value of $g(x)$ into the function.

Substituting the Value of $g(x)$

$g(x) = -6$

$-\frac{-1 + x}{4} = -6$

Multiplying Both Sides by 4

$-1 + x = -24$

Adding 1 to Both Sides

$x = -23$

Checking the Solution

To check our solution, we will plug the value of $x$ back into the original equation.

$g(-23) = -\frac{-1 + (-23)}{4}$

$g(-23) = -\frac{-24}{4}$

$g(-23) = 6$

Since $g(-23) = 6$, our solution is correct.

Conclusion

In this article, we have solved for $x$ in the function $g(x) = -\frac{-1 + x}{4}$ when $g(x) = -6$. We have broken down the steps involved in solving this problem and provided a clear explanation of each step. The final solution is $x = -23$.

Final Answer

The final answer is $\boxed{-23}$.

Additional Information

• The function $g(x) = -\frac{-1 + x}{4}$ is a linear function.
• The value of $g(x)$ is equal to $-6$ when $x = -23$.
• To solve for $x$, we need to substitute the value of $g(x)$ into the function and then simplify the equation.

Related Topics

• Solving linear equations
• Substituting values into functions
• Simplifying equations

References

• Linear Equations
• Functions
• Simplifying Equations
  

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Introduction

In our previous article, we solved for $x$ in the function $g(x) = -\frac{-1 + x}{4}$ when $g(x) = -6$. In this article, we will provide a Q&A section to help clarify any questions or doubts that readers may have.

Q&A

Q: What is the function $g(x) = -\frac{-1 + x}{4}$?

A: The function $g(x) = -\frac{-1 + x}{4}$ is a linear function that takes an input $x$ and returns an output $g(x)$.

Q: What is the value of $g(x)$ when $x = -23$?

A: The value of $g(x)$ when $x = -23$ is $-6$.

Q: How do we solve for $x$ in the function $g(x) = -\frac{-1 + x}{4}$?

A: To solve for $x$, we need to substitute the value of $g(x)$ into the function and then simplify the equation.

Q: What is the final solution for $x$?

A: The final solution for $x$ is $-23$.

Q: How do we check the solution?

A: To check the solution, we need to plug the value of $x$ back into the original equation to see if it is true.

Q: What is the significance of the function $g(x) = -\frac{-1 + x}{4}$?

A: The function $g(x) = -\frac{-1 + x}{4}$ is a linear function that can be used to model real-world situations.

Q: What are some related topics to this problem?

A: Some related topics to this problem include solving linear equations, substituting values into functions, and simplifying equations.

Q: Where can I find more information on this topic?

A: You can find more information on this topic by visiting the following websites:

• Linear Equations
• Functions
• Simplifying Equations

Conclusion

In this article, we have provided a Q&A section to help clarify any questions or doubts that readers may have. We have also provided some related topics and resources for further learning.

Final Answer

The final answer is $\boxed{-23}$.

Additional Information

• The function $g(x) = -\frac{-1 + x}{4}$ is a linear function.
• The value of $g(x)$ is equal to $-6$ when $x = -23$.
• To solve for $x$, we need to substitute the value of $g(x)$ into the function and then simplify the equation.

Related Topics

• Solving linear equations
• Substituting values into functions
• Simplifying equations

References

• Linear Equations
• Functions
• Simplifying Equations