Given The Linear Function F ( X ) = − 4 X + 8 F(x)=-4x+8 F ( X ) = − 4 X + 8 , What Is The Value Of X X X If F ( X ) = 24 F(x)=24 F ( X ) = 24 ?A. X = 104 X=104 X = 104 B. X = − 4 X=-4 X = − 4 C. X = − 8 X=-8 X = − 8 D. X = − 88 X=-88 X = − 88

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Introduction

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Linear equations are a fundamental concept in mathematics, and solving them is a crucial skill for students and professionals alike. In this article, we will focus on solving linear equations of the form $f(x) = mx + b$, where $m$ is the slope and $b$ is the y-intercept. We will use the given linear function $f(x)=-4x+8$ to find the value of $x$ when $f(x)=24$.

Understanding Linear Functions

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A linear function is a polynomial function of degree one, which means it can be written in the form $f(x) = mx + b$. The slope $m$ represents the rate of change of the function, and the y-intercept $b$ represents the point where the function intersects the y-axis.

In the given function $f(x)=-4x+8$, the slope $m$ is $-4$, and the y-intercept $b$ is $8$. This means that for every unit increase in $x$, the value of $f(x)$ decreases by $4$ units.

Solving Linear Equations

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To solve a linear equation of the form $f(x) = mx + b$, we need to isolate the variable $x$. We can do this by adding or subtracting the same value to both sides of the equation, or by multiplying or dividing both sides by the same non-zero value.

In this case, we are given the equation $f(x) = 24$, and we need to find the value of $x$. We can start by substituting the given function $f(x)=-4x+8$ into the equation:

$$-4x+8=24$$

Isolating the Variable

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To isolate the variable $x$, we need to get rid of the constant term $8$ on the left-hand side of the equation. We can do this by subtracting $8$ from both sides of the equation:

$$-4x=-4x+8-8$$

$$-4x=-4$$

Solving for x

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Now that we have isolated the variable $x$, we can solve for its value. We can do this by dividing both sides of the equation by $-4$:

$$x=\frac{-4}{-4}$$

$$x=1$$

However, this is not the correct answer. We need to go back to the original equation and try a different approach.

Using the Given Function

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Let's go back to the original equation $f(x)=-4x+8$ and substitute $f(x)=24$:

$$-4x+8=24$$

Isolating the Variable (Again)

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To isolate the variable $x$, we need to get rid of the constant term $8$ on the left-hand side of the equation. We can do this by subtracting $8$ from both sides of the equation:

$$-4x=-4x+8-8$$

$$-4x=16$$

Solving for x (Again)

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Now that we have isolated the variable $x$, we can solve for its value. We can do this by dividing both sides of the equation by $-4$:

$$x=\frac{16}{-4}$$

$$x=-4$$

Conclusion

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In this article, we used the given linear function $f(x)=-4x+8$ to find the value of $x$ when $f(x)=24$. We started by substituting the given function into the equation and then isolated the variable $x$ by subtracting $8$ from both sides of the equation. Finally, we solved for the value of $x$ by dividing both sides of the equation by $-4$. The correct answer is $x=-4$.

Final Answer

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The final answer is $x=-4$.

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Introduction

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In our previous article, we discussed how to solve linear equations of the form $f(x) = mx + b$. We used the given linear function $f(x)=-4x+8$ to find the value of $x$ when $f(x)=24$. In this article, we will provide a Q&A guide to help you understand and solve linear equations.

Q&A

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Q: What is a linear equation?

A: A linear equation is a polynomial equation of degree one, which means it can be written in the form $f(x) = mx + b$. The slope $m$ represents the rate of change of the function, and the y-intercept $b$ represents the point where the function intersects the y-axis.

Q: How do I solve a linear equation?

A: To solve a linear equation, you need to isolate the variable $x$. You can do this by adding or subtracting the same value to both sides of the equation, or by multiplying or dividing both sides by the same non-zero value.

Q: What is the slope-intercept form of a linear equation?

A: The slope-intercept form of a linear equation is $f(x) = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

Q: How do I find the value of $x$ in a linear equation?

A: To find the value of $x$, you need to isolate the variable $x$ by getting rid of the constant term on the left-hand side of the equation. You can do this by subtracting the constant term from both sides of the equation.

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

A: A linear equation is a polynomial equation of degree one, while a quadratic equation is a polynomial equation of degree two. A linear equation can be written in the form $f(x) = mx + b$, while a quadratic equation can be written in the form $f(x) = ax^2 + bx + c$.

Q: How do I determine the slope of a linear equation?

A: To determine the slope of a linear equation, you need to look at the coefficient of the $x$ term. The slope is the value of the coefficient.

Q: What is the y-intercept of a linear equation?

A: The y-intercept of a linear equation is the point where the function intersects the y-axis. It is the value of $b$ in the equation $f(x) = mx + b$.

Examples

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Example 1: Solving a Linear Equation

Solve the equation $f(x) = 2x + 3$ when $f(x) = 5$.

f(x) = 2x + 3
5 = 2x + 3
2x = 5 - 3
2x = 2
x = 1

Example 2: Finding the Slope of a Linear Equation

Find the slope of the equation $f(x) = 3x - 2$.

f(x) = 3x - 2
The slope is the coefficient of the x term, which is 3.

Example 3: Finding the Y-Intercept of a Linear Equation

Find the y-intercept of the equation $f(x) = 2x + 5$.

f(x) = 2x + 5
The y-intercept is the value of b, which is 5.

Conclusion

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In this article, we provided a Q&A guide to help you understand and solve linear equations. We discussed the slope-intercept form of a linear equation, how to solve a linear equation, and how to find the value of $x$. We also provided examples to help you understand the concepts.

Final Answer

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The final answer is that linear equations are a fundamental concept in mathematics, and solving them is a crucial skill for students and professionals alike. By understanding the slope-intercept form of a linear equation, how to solve a linear equation, and how to find the value of $x$, you can solve linear equations with ease.