Solve For { X $}$ Given The Function Output.Function: { H(x) = 2 - 6x $}$1. If { H(x) = -4 $}$, Then Solve For { X $}$: ${ 2 - 6x = -4 }$ { X = \square $} 2. I F \[ 2. If \[ 2. I F \[ H(x) =

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Introduction

In mathematics, solving for a variable in a function is a fundamental concept that is used extensively in various fields such as physics, engineering, and economics. Given a function output, we need to find the value of the input that produces that output. In this article, we will focus on solving for { x $}$ given the function output using a linear function.

Linear Function

A linear function is a function that can be written in the form { f(x) = mx + b $}$, where { m $}$ is the slope and { b $}$ is the y-intercept. In this article, we will use the linear function { h(x) = 2 - 6x $}$.

Solving for { x $}$

To solve for { x $}$, we need to isolate { x $}$ on one side of the equation. We can do this by adding { 6x $}$ to both sides of the equation and then dividing both sides by { 6 $}$.

Example 1: { h(x) = -4 $}$

If { h(x) = -4 $}$, then we can set up the equation { 2 - 6x = -4 $}$. To solve for { x $}$, we need to isolate { x $}$ on one side of the equation.

2 - 6x = -4

We can start by adding { 6x $}$ to both sides of the equation:

2 - 6x + 6x = -4 + 6x

This simplifies to:

2 = -4 + 6x

Next, we can add { 4 $}$ to both sides of the equation:

2 + 4 = -4 + 4 + 6x

This simplifies to:

6 = 6x

Finally, we can divide both sides of the equation by { 6 $}$:

x = 6/6

This simplifies to:

x = 1

Therefore, if { h(x) = -4 $}$, then { x = 1 $}$.

Example 2: { h(x) = 0 $}$

If { h(x) = 0 $}$, then we can set up the equation { 2 - 6x = 0 $}$. To solve for { x $}$, we need to isolate { x $}$ on one side of the equation.

2 - 6x = 0

We can start by adding { 6x $}$ to both sides of the equation:

2 - 6x + 6x = 0 + 6x

This simplifies to:

2 = 6x

Next, we can divide both sides of the equation by { 6 $}$:

x = 2/6

This simplifies to:

x = 1/3

Therefore, if { h(x) = 0 $}$, then { x = 1/3 $}$.

Example 3: { h(x) = 1 $}$

If { h(x) = 1 $}$, then we can set up the equation { 2 - 6x = 1 $}$. To solve for { x $}$, we need to isolate { x $}$ on one side of the equation.

2 - 6x = 1

We can start by adding { 6x $}$ to both sides of the equation:

2 - 6x + 6x = 1 + 6x

This simplifies to:

2 = 1 + 6x

Next, we can subtract { 1 $}$ from both sides of the equation:

2 - 1 = 1 - 1 + 6x

This simplifies to:

1 = 6x

Finally, we can divide both sides of the equation by { 6 $}$:

x = 1/6

Therefore, if { h(x) = 1 $}$, then { x = 1/6 $}$.

Conclusion

In this article, we have shown how to solve for { x $}$ given the function output using a linear function. We have used three examples to illustrate the process of solving for { x $}$. By following the steps outlined in this article, you should be able to solve for { x $}$ given the function output.

References

Discussion

Introduction

In our previous article, we discussed how to solve for { x $}$ given the function output using a linear function. In this article, we will answer some frequently asked questions (FAQs) related to solving for { x $}$ given the function output.

Q&A

Q: What is the first step in solving for { x $}$ given the function output?

A: The first step in solving for { x $}$ given the function output is to set up the equation by equating the function output to the given value.

Q: How do I isolate { x $}$ on one side of the equation?

A: To isolate { x $}$ on one side of the equation, you need to add or subtract the same value to both sides of the equation, and then divide both sides of the equation by the coefficient of { x $}$.

Q: What if the equation has a fraction?

A: If the equation has a fraction, you can multiply both sides of the equation by the denominator to eliminate the fraction.

Q: Can I use a calculator to solve for { x $}$?

A: Yes, you can use a calculator to solve for { x $}$. However, it's always a good idea to check your work by plugging the solution back into the original equation.

Q: What if I get a negative value for { x $}$?

A: If you get a negative value for { x $}$, it means that the solution is not valid. You need to recheck your work and try again.

Q: Can I use this method to solve for { x $}$ in a quadratic equation?

A: No, this method is only applicable to linear equations. To solve for { x $}$ in a quadratic equation, you need to use a different method, such as factoring or the quadratic formula.

Q: How do I know if the solution is valid?

A: To check if the solution is valid, you need to plug the solution back into the original equation and check if it's true.

Q: Can I use this method to solve for { x $}$ in a system of equations?

A: No, this method is only applicable to a single equation. To solve for { x $}$ in a system of equations, you need to use a different method, such as substitution or elimination.

Examples

Example 1: Solving for { x $}$ in a linear equation

Suppose we have the equation { 2x + 3 = 5 $}$. To solve for { x $}$, we need to isolate { x $}$ on one side of the equation.

2x + 3 = 5

We can start by subtracting { 3 $}$ from both sides of the equation:

2x + 3 - 3 = 5 - 3

This simplifies to:

2x = 2

Next, we can divide both sides of the equation by { 2 $}$:

x = 2/2

This simplifies to:

x = 1

Therefore, the solution to the equation is { x = 1 $}$.

Example 2: Solving for { x $}$ in a quadratic equation

Suppose we have the equation { x^2 + 4x + 4 = 0 $}$. To solve for { x $}$, we need to use a different method, such as factoring or the quadratic formula.

x^2 + 4x + 4 = 0

We can start by factoring the left-hand side of the equation:

(x + 2)(x + 2) = 0

This simplifies to:

(x + 2)^2 = 0

Next, we can take the square root of both sides of the equation:

x + 2 = 0

This simplifies to:

x = -2

Therefore, the solution to the equation is { x = -2 $}$.

Conclusion

In this article, we have answered some frequently asked questions (FAQs) related to solving for { x $}$ given the function output. We have also provided examples of how to solve for { x $}$ in a linear equation and a quadratic equation. By following the steps outlined in this article, you should be able to solve for { x $}$ given the function output.

References

Discussion

What are some other ways to solve for { x $}$ given the function output? How can you apply the concepts learned in this article to real-world problems? Share your thoughts and ideas in the comments below!